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Bibliography on the evaluation of numerical software. (English) Zbl 0399.65003

MSC:

65-04 Software, source code, etc. for problems pertaining to numerical analysis
00A15 Bibliographies for mathematics in general
68N99 Theory of software
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[1] Amster, S.J.; Dickman, B.N., An experiment in automatic quality evaluation of software, ()
[2] Bailey, Carl B.; Jones, Rondall E., Usage and argument monitoring of mathematical library routines, ACM transactions on mathematical software, Vol. 1, 196-209, (1975)
[3] Barth, Jeffrey M., A practical interprocedural data flow analysis algorithm, Communications of the ACM, Vol. 21, 724-736, (1978)
[4] Bate, Roger R.; Ligler, George T., An approach to software testing: methodology and tools, (), 476-480
[5] Bright, H.S.; Cole, I.J., A method of testing programs for data sensitivity, (), 143-162
[6] Brown, J.R.; Hoffman, R.H., Evaluating the effectiveness of software verification — practical experience with an automated tool, (), 181-190
[7] Brown, W.Stanley, Some fundamentals of performance evaluation for numerical software, (), to be published by
[8] Chen, Wen-Tsuen; Ho, Jone-Ping; Wen, Chia-Hsien, Dynamic validation of programs using assertion checking facilities, (), 533-538
[9] Clarke, Lori A., A system to generate test data and symbolically execute programs, IEEE transactions on software engineering, Vol. SE-2, 215-222, (1976)
[10] Clarke, Lori A., Testing: achievements and frustrations, (), 310-314
[11] Cody, W.J., The evaluation of mathematical software, (), 121-133
[12] Cody, W.J., The construction of numerical subroutine libraries, SIAM review, Vol. 16, 36-46, (1974) · Zbl 0272.68032
[13] Cody, W.J., Mathematical software — why the fuss, (), 378, Abstract in
[14] Cohen, Jacques; Carpenter, Neal, A language for inquiring about the run-time behaviour of programs, Software — practice and experience, Vol. 7, 445-460, (1977) · Zbl 0361.68017
[15] ()
[16] Cowell, Wayne R., The validation of mathematical software, (), 534
[17] Cowell, W.R.; Fosdick, L.D., Mathematical software production, (), 195-224
[18] Crowder, H.P.; Dembo, R.S.; Mulvey, J.M., On reporting computational experiments with mathematical software, ACM transactions on mathematical software, Vol. 5, (1979), to appear
[19] Dekker, Theodorus J., Correctness proof and machine arithmetic, (), to be published by
[20] Einarsson, Bo, Utvärdering av matematisk programvara — en kombination av matematik, numerisk analys, datalogi och informationsteknik, (), in Swedish
[21] Einarsson, Bo, The applicability of data flow analysis to different programming languages, () · Zbl 0900.68103
[22] Einarsson, Bo, Solving a system of linear inequalities for generating test data, Journal of computational and applied mathematics, Vol. 3, 269-271, (1977) · Zbl 0368.68023
[23] Fairley, Richard E., An experimental program testing facility, IEEE transactions on software engineering, Vol. SE-1, 350-357, (1975)
[24] Fitzsimmons, Ann; Love, Tom, A review and evaluation of software science, Computing surveys, Vol. 10, 3-18, (1978) · Zbl 0373.68017
[25] Ford, Brian, Some transformations of numerical software, (), 381, Abstract in
[26] Ford, Brian; Hodgson, Graham S.; Sayers, David K., Evaluation of numerical software for many machines — is it possible?, (), to be published by
[27] Forsythe, George E.; Malcolm, Michael A.; Moler, Cleve B., Computer methods for mathematical computations, (), 259 · Zbl 0361.65002
[28] Fosdick, Lloyd D.; Osterweil, Leon J., DAVE — A FORTRAN program analysis system, (), 329-335 · Zbl 0329.68011
[29] Fosdick, Lloyd D.; Osterweil, Leon J., Data flow analysis in software reliability, Computing surveys, Vol. 8, 305-330, (1976) · Zbl 0359.68022
[30] Fosdick, Lloyd D.; Osterweil, Leon J., The detection of anomalous interprocedural data flow, () · Zbl 0359.68022
[31] Fosdick, Lloyd D., Detecting errors in software, (), to be published by
[32] Fox, P.A.; Hall, A.D.; Schryer, N.L., The PORT mathematical subroutine library, ACM transactions on mathematical software, Vol. 4, 104-126, (1978)
[33] Francis, I.; Heiberger, P.M.; Velleman, P.F., Criteria and considerations in the evaluation of statistical program packages, Amer. station., Vol. 29, 52-56, (1975)
[34] Francis, I., Design for evaluation of statistical program packages, Bull. intl. stat. inst., Vol. 46, 573-584, (1975)
[35] Gary, John M., Analysis of applications programs and software requirements for high speed computers, (), 329-354, 1977
[36] Geller, Matthew, Test data as an aid in proving program correctness, Communications of the ACM, Vol. 21, 368-375, (1978) · Zbl 0372.68002
[37] Gepner, Herbert L., User ratings of software packages, Datamation, 163-227, (1978), December 1978
[38] Gilb, Tom, Software metrics, (1977), Winthrop Publishers Cambridge, Massachusetts · Zbl 0770.68004
[39] Ginsberg, M., A review of supercomputers for scientific computation, (), 8, No. 4 (December 1977)
[40] Ginsberg, Myron, Numerical influences on the design of floating-point arithmetic for microcomputers, (), 24-72
[41] Goodenough, J.B., A survey of program testing issues, (), 135-154, Part 2
[42] Halstead, Maurice H., Elements of software science, operating and programming systems series, (), 127
[43] Hammer, C., Statistical validation of mathematical computer routines, (), 311-333
[44] Heath, M.T.; Funderlic, R.E., The organization of our numerical software library (union carbide corporatiion, oak ridge), ()
[45] Heiberger, Richard M., A procedure for the review of statistical packages and its application to the user interface with regression programs, (), 115-121
[46] Hennell, M.A., An experimental testbed for numerical software, The computer journal, Vol. 21, 333-336, (1978)
[47] Hetzel, William C., Principles of computer program testing, (), 17-28
[48] Hoaglin, David C., Mathematical software and exploratory data analysis, (), 139-159 · Zbl 0407.68032
[49] Howden, William E., Theoretical and empirical studies of program testing, IEEE transactions on software engineering, Vol. SE-4, 293-298, (1978) · Zbl 0383.68017
[50] Hull, Tom E., Correctness of numerical software, (), to be published by
[51] Hoyt, Patrick M., The navy Fortran validation system, (), 529-537
[52] Ivie, Evan L., The Programmer’s workbench — A machine for software development, Communications of the ACM, Vol. 20, 746-753, (1977)
[53] King, James C., Prospects for program verification, tutorial session, (), 71
[54] Knuth, D.E., An empirical study of FORTRAN programs, Software — practice and experience, Vol. 1, 105-133, (1971) · Zbl 0243.68003
[55] Krogh, Fred T., A plea for tolerance in the evaluation of numerical methods and mathematical software, SIGNUM newsletter, Vol. 6, No. 3, 7-8, (1971), November 1971
[56] Lim, Ṙ.T.C.; Blackburn, J.D., On program verification in numerical methods, letter ot the editor, The computer journal, Vol. 19, 272-273, (1976) · Zbl 0334.65036
[57] Lyness, James, Performance profile and software evaluation, (), to be published by
[58] Miller, E.F., RXVP: an automated verification system for FORTRAN, (), 328
[59] Miller, Edward F.; Miller, Edward F.; Howden, William E., Program testing techniques, tutorial, IEEE catalog no. EHO 130-5, Software testing and validation techniques, 428, (1978), with the title
[60] Miller, Edward F., Special issue on program testing of the IEEE computer, Vol. 11, No. 4, 10-60, (1978)
[61] Miller, Edward F., Program testing — an overview for managers, (), 114-119
[62] Miller, Webb C.; Spooner, David, Automatic generation of floating-point test data, IEEE transactions on software engineering, Vol. SE-2, 223-226, (1976)
[63] Mills, H.D., On the statistical validation of computer programs, IBM report FSC-72-6015, 16, (1970)
[64] Mohanty, S.N., Proposed measures for evaluation of software, ()
[65] Nelder, J.A., Experimental design and statistical evaluation, (), to be published by · Zbl 0293.68040
[66] Ng, E.W., Mathematical software testing activities, (), 135-141
[67] Osterweil, Leon; Fosdick, Lloyd D., Automated input/output variable classification as an aid to validation of Fortran programs, () · Zbl 0329.68011
[68] Osterweil, Leon, Depth-first search techniques and efficient methods for creating test paths, () · Zbl 0504.68011
[69] Osterweil, Leon J.; Fosdick, Lloyd D., Some experience with DAVE—A Fortran program analyzer, () · Zbl 0329.68011
[70] Osterweil, Leon J., A proposal for an integrated testing system for computer programs, ()
[71] Osterweil, Leon J.; Fosdick, Lloyd D., DAVE — A validation, error detection, and documentation system for Fortran programs, Software — practice and experience, Vol. 6, 473-486, (1976) · Zbl 0329.68011
[72] Paige, Michael R., An analytical approach to software testing, (), 527-532
[73] Parlett, Beresford, Progress in numerical analysis, SIAM review, Vol. 20, 443-456, (1978) · Zbl 0408.65002
[74] Rice, John R., TOMS policy statement, the rights of program authors in the evaluation of programs, ACM transactions on mathematical software, Vol. 2, 113-114, (1976)
[75] Rice, John R., The algorithm selection problem, (), 65-118, 1976
[76] Rice, John R., Software for numerical computation, (), 1 · Zbl 0327.65025
[77] Rice, John R., Methodology for the algorithm selection problem, (), to be published by
[78] Richards, F.R., Computer software: testing, reliability models, and quality assurance, (), 80
[79] Rosen, Barry K., High-level data flow analysis, Communications of the ACM, Vol. 20, 712-724, (1977) · Zbl 0399.68014
[80] Sameh, Ahmed H., Numerical parallel algorithms — A survey, (), 207-228, 1977
[81] Schaefer, Marvin, A mathematical theory of global program optimization, (), 198 · Zbl 0354.68003
[82] Stetter, Hans J., Aspects of man-software communication, (), 398, Abstract in
[83] Taylor, Richard N.; Osterweil, Leon J., A facility for verification, testing and documentation of concurrent process software, (), 36-41
[84] Usow, Karl H.; Usow, Karl H., Certification bibliography, SIGNUM newsletter, SIGNUM newsletter, Vol. 5, No. 2, 14-15, (1969), August 1970
[85] Usow, Karl H.; Fosdick, Lloyd D., Guidelines for evaluating an algorithm for publication, SIGNUM newsletter, Vol. 4, No. 3, 19-20, (1969), October 1969
[86] Voigt, Robert G., The influence of vector computer architecture on numerical algorithms, (), 229-244
[87] Wasserman, Anthony I.; Belady, L.A., Software engineering: the turning point, Computer (IEEE), Vol. 11, 30-41, (1978), (September 1978)
[88] Weide, Bruce, A survey of analysis techniques for discrete algorithms, Computing surveys, Vol. 9, 291-313, (1977) · Zbl 0366.68040
[89] Weinberg, Gerald M., The psychology of computer programming, (), 298
[90] Wichmann, B.A., Estimating the execution speed of an algol program, National physical laboratory, NPL report NAC 38, (1973), June 1973 · Zbl 0278.68010
[91] Wirsching, J.E.; Kishi, T., Matching machines and problems, (), 379-397
[92] Sorting 30 times faster with DPS (distributive partitioning sort), Datamation, 200-203, (1978), February 1978
[93] Sort scoop settled (editorial and letters by zimmer, dobosiewicz, and ferguson), Datamation, Datamation, 34, (1978), August 1978
[94] Atkinson, A.C.; Pearce, M.C., The computer generation of beta, gamma and normal random variables, J. roy. statist. soc. A, Vol. 139, 431-461, (1976), Part 4
[95] Barinka, L.L.; Neves, K.W.; Tuttle, P.G., Performance of some vectorized mathematical software, (), 794, Abstract in
[96] Barinka, L.L.; Connelly, W.H.; Thompson, S.; Tuttle, P.G., Performance of some vectorized mathematical software, (), 375-376, Abstract in
[97] de Boor, Carl, A comment on “numerical comparisons of algorithms for polynomial and rational multivariate approximations”, SIAM journal on numerical analysis, Vol. 15, 1208-1211, (1978) · Zbl 0414.65009
[98] Dobosiewicz, Woldzmierz, Sorting by distributive partitioning, Information processing letters, Vol. 7, No. 1, 1-6, (1978), (January 1978) · Zbl 0373.68034
[99] Francis, Ivor, A bibliography for statistical software: reviews, evaluations, standards and improvements, ()
[100] Franke, Richard, Comparison of some local methods for interpolation of scattered data, () · Zbl 0476.65005
[101] Galantai, Aurel, The comparison of numerical methods for solving polynomial equations, Mathematics of computation, Vol. 32, 391-397, (1978) · Zbl 0375.65026
[102] Gautschi, Walter, Anomalous convergence of a continued fraction for ratios of Kummer functions, Mathematics of computation, Vol. 31, 994-999, (1977) · Zbl 0373.33002
[103] Ginsberg, Myron, Some numerical effects of a FORTRAN vectorizing compiler on a Texas instruments advanced scientific computer, (), 461-462, 1977
[104] Gonnet, Gaston H., On the structure of zero finders, Bit, Vol. 17, 170-183, (1977) · Zbl 0365.65029
[105] Henry, Jackson N., Comparison of algorithms for multivariate rational approximation, Mathematics of computation, Vol. 31, 485-494, (1977) · Zbl 0356.65009
[106] Henry, J.N.; Henry, M.S.; Schmidt, D., Numerical comparisons of algorithms for polynomial and rational multivariate approximations, SIAM journal on numerical analysis, Vol. 15, 1197-1207, (1978) · Zbl 0414.65008
[107] Howden, William E., An evaluation of the effectiveness of symbolic testing, Software — practice and experience, Vol. 8, 381-397, (1978) · Zbl 0376.68024
[108] Jenkins, M.A.; Traub, J.F., Principles for testing polynomial zerofinding programs, ACM transactions on mathematical software, Vol. 1, 26-34, (1975) · Zbl 0311.65039
[109] Kuki, H.; Cody, W.J., A statistical study of the accuracy of floating point number systems, Communications of the ACM, Vol. 16, 223-230, (1973) · Zbl 0271.65031
[110] Leece, John; Parker, Frank, Use of misuse of SPSS, Software-practice and experience, Vol. 8, 301-311, (1978)
[111] Loeser, R., Some performance test of “quicksort” and descendants, Communications of the ACM, Vol. 17, No. 3, 143-152, (1974)
[112] Loeser, Rudolf, Survey on algorithms 347, 426, and quicksort, ACM transactions on mathematical software, Vol. 2, 290-299, (1976)
[113] Myers, Glenford J., A controlled experiment in program testing and code walkthroughs/inspections, Communications of the ACM, Vol. 21, 760-768, (1978)
[114] Parker, D.Stott, Nonlinear recurrences and parallel computation, (), 317-320, 1977
[115] Payne, W.H., Normal random numbers: using machine analysis to choose the best algorithm, ACM transactions on mathematical software, Vol. 3, 346-358, (1977) · Zbl 0374.68038
[116] Remund, R.N.; Taggart, K.A., To vectorize or to “vectorize”: that is the question, (), 399-410, 1977
[117] Slysz, W.D., An evaluation of statistical software in the social sciences, Communications of the ACM, Vol. 17, No. 6, 326-332, (1974)
[118] Sparks, Paul R.; Sparks, Paul R.; Sparks, Paul R., Sorting out sorting (letter), Datamation, Datamation, Datamation, 319, (1978), May 1978
[119] Stone, Harold S., Sorting on STAR, IEEE transactions on software engineering, Vol. SE-4, 138-146, (1978) · Zbl 0381.68058
[120] Tessler, Harvey B., More on sorting (letter), Datamation, 26, (1978), July 1978
[121] Axelsson, Owe, A class of iterative methods for finite element equations, Computer methods in applied mechanics and engineering, Vol. 9, No. 2, 133-137, (1976)
[122] Barinka, Lawrence L., Some experience with constructing, testing, and certifying a standard mathematical subroutine library, ACM transactions on mathematical software, Vol. 1, 165-177, (1975) · Zbl 0303.68027
[123] Barwell, Victor; George, Alan, A comparison of algorithms for solving symmetric indefinite systems of linear equations, ACM transactions on mathematical software, Vol. 2, 242-251, (1976) · Zbl 0332.65016
[124] Blaser, A.; Schauer, U., Performance measurements on the sparse matrix subroutines of SL-math, (), 301
[125] Bunch, James R.; Kaufman, Linda, Some stable methods for calculating inertia and solving symmetric linear systems, Mathematics of computation, Vol. 31, 163-179, (1977) · Zbl 0355.65023
[126] Cabay, S.; Lam, T.P.L., Congruence techniques for the exact solution of integer systems of linear equations, ACM transactions on mathematical software, Vol. 3, 386-397, (1977) · Zbl 0374.68035
[127] Chan, Chorkin; Klassen, Melvin, A performance comparison study between subroutine packages LINSYS, IBMSSP and IMSL for solving systems of linear equations, Journal of computational and applied mathematics, Vol. 1, No. 2, 111-113, (1975) · Zbl 0301.65016
[128] Chen, S.C.; Kuck, D.J.; Sameh, A.H., Practical parallel band triangular system solvers, ACM transactions on mathematical software, Vol. 4, 270-277, (1978) · Zbl 0384.65013
[129] Cline, A.K.; Moler, C.B.; Stewart, G.W.; Wilkinson, J.H., An estimate for the condition number of a matrix, () · Zbl 0403.65012
[130] Concus, P.; Golub, G.H.; O’Leary, D.P., Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method, Computing, Vol. 19, 321-339, (1978) · Zbl 0385.65048
[131] Dembart, B.; Neves, K.W., Sparse triangular factorization on vector computers, SIGNUM newsletter, Vol. 12, No. 4, 6, (1977), (December 1977)
[132] Dongarra, J.J., Fortran BLAS timing, ()
[133] Dongarra, J.J., Some LINPACK timings on the CRAY-1, ()
[134] Duff, I.S.; Reid, J.K., A comparison of some methods for the solution of sparse overdetermined systems of linear equations, Journal of the institute of mathematics and its applications, Vol. 17, 267-280, (1976) · Zbl 0329.65026
[135] Duff, I.S.; Erisman, A.M.; Reid, J.K., On George’s nested dissection method, SIAM journal on numerical analysis, Vol. 13, 686-695, (1976) · Zbl 0345.65015
[136] Duff, I.S., Practical comparisons of codes for the solution of sparse linear systems, () · Zbl 0437.65024
[137] Duff, Iain S.; Reid, John K., Performance evaluation of codes for sparse matrix problems, (), to be published by
[138] Eisenstat, S.C.; Schultz, M.H.; Sherman, A.H., Application of sparse matrix methods to partial differential equations, (), 40-45, Available from · Zbl 0297.65054
[139] Eisenstat, S.C.; Schultz, M.H.; Sherman, A.H., An auxiliary storage method for solving large sparse positive definite systems of linear equations, Presented at the SIGNUM meeting on mathematical software, 3-4 November 1977, Albuquerque, New Mexico, SIGNUM newsletter, Vol. 12, 4, (1977), No. 4, December 1977
[140] Eisenstat, S.C.; Schultz, M.H.; Sherman, A.H., Minimal storage band elimination, (), 273-286, 1977
[141] Elfving, Tommy, On computing generalized solutions of sparse linear systems with application to some reconstruction problems, (), No. 27 · Zbl 1062.65041
[142] Evans, D.J., The analysis and application of sparse matrix algorithms in the finite element method, (), 427-447
[143] Fitzgerald, Kenneth E., Comparison of some FORTRAN programs for matrix inversion, Journal of research of the national bureau of standards- B. mathematical sciences, Vol. 78B, No. 1, 15-23, (1974) · Zbl 0281.65024
[144] Garbow, B.S.; Boyle, J.M.; Dongarra, J.J.; Moler, C.B., Matrix eigensystem routines — EISPACK guide extension, (), 343 · Zbl 0368.65020
[145] George, Alan, Numerical experiments using dissection methods to solve n by n grid problems, SIAM journal on numerical analysis, Vol. 14, 161-179, (1977) · Zbl 0356.65023
[146] George, Alan; Liu, Joseph W.H., Algorithms for matrix partitioning and the numerical solution of finite element systems, SIAM journal on numerical analysis, Vol. 15, 297-327, (1978) · Zbl 0389.65015
[147] George, Alan; Liu, Joseph W.H., An automatic nested dissection algorithm for irregular finite element problems, SIAM journal on numerical analysis, Vol. 15, 1053-1069, (1978) · Zbl 0408.65064
[148] George, Alan; Poole, William G.; Voigt, Robert G., Incomplete nested dissection for solving n by n grid problems, SIAM journal on numerical analysis, Vol. 15, 662-673, (1978) · Zbl 0393.65014
[149] Gibbs, Norman E.; Poole, William G.; Stockmeyer, Paul K., A comparison of several bandwidth and profile reduction algorithms, ACM transactions on mathematical software, Vol. 2, 322-330, (1976) · Zbl 0345.65014
[150] Goodman, J.T.; Moler, C.B., Three numerical experiments with Gaussian elimination, ()
[151] Gustafsson, Ivar, A class of first order factorization methods, Bit, Vol. 18, 142-156, (1978) · Zbl 0386.65006
[152] Gustavson, Fred G., Two fast algorithms for sparse matrices: multiplication and permuted transposition, ACM transactions on mathematical software, Vol. 4, 250-269, (1978) · Zbl 0384.65016
[153] Hanson, Richard J., Certifying linear algebra solvers, SIGNUM newsletter, Vol. 4, No. 3, 21-27, (1969), October 1969
[154] Heller, D.E.; Stevenson, D.K.; Traub, J.F., Accelerate iterative methods for the solution of tridiagonal systems on parallel computers, Journal of the association for computing machinery, Vol. 23, 636-654, (1976) · Zbl 0347.65021
[155] Heller, Don, A survey of parallel algorithms in numerical linear algebra, SIAM review, Vol. 20, 740-777, (1978) · Zbl 0408.68033
[156] Johnson, A.I.; Barney, J.R., Numerical solution of large systems of stiff ordinary differential equations in a modular simulation framework, (), 97-124
[157] Jordan, T.L.; Fong, Kirby, Some linear algebraic algorithms and their performance on CRAY-1, (), 313-316, 1977
[158] Jordan, Thomas L., A performance evaluation of linear algebra software in parallel architecture, (), to be published by
[159] Kershaw, David S., The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations, Journal of computational physics, Vol. 26, 43-65, (1978) · Zbl 0367.65018
[160] Kågström, Bo., Bounds and perturbation bounds for the matrix exponential, Bit, Vol. 17, 39-57, (1977) · Zbl 0356.65034
[161] Kågström, Bo., Numerical computation of matrix functions, () · Zbl 0542.65021
[162] Lambiotte, Jules J.; Voigt, Robert G., The solution of tridiagonal linear systems on the CDC STAR-100 computer, ACM transactions on mathematical software, Vol. 1, 308-329, (1975) · Zbl 0315.65019
[163] Lawson, C.L., Standardization of Fortran callable subprograms for basic linear algebra, (), 261
[164] Lawson, C.L.; Ekelund, J., An out-of-core least squares program, (), 5, No. 4 (December 1977)
[165] Madsen, Niel K.; Rodrigue, Garry H., A comparison of direct methods for tridiagonal systems on the CDC STAR-100, (1976), Lawrence Livermore Laboratory, Preprint UCRL-76993, Rev. 1, May 1976 · Zbl 0337.65024
[166] McClellan, M.T., The exact solution of systems of linear equations with polynomial coefficients, Journal of the association for computing machinery, Vol. 20, 563-588, (1973) · Zbl 0273.65030
[167] McClellan, Michael T., The exact solution of linear equations with rational function coefficients, ACM transactions on mathematical software, Vol. 3, 1-25, (1977) · Zbl 0348.65029
[168] McClellan, Michael T., A comparison of algorithms for the exact solution of linear equations, ACM transactions on mathematical software, Vol. 3, 147-158, (1977) · Zbl 0364.65022
[169] Meijerink, J.A.; van der Vorst, H.A., An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Mathematics of computation, Vol. 31, 148-162, (1977) · Zbl 0349.65020
[170] Molchanov, Igor, Performance evaluation of linear algebra software, (), to be published by
[171] Moler, Cleve B., Software for matrix computations, (), 307-321
[172] Moler, Cleve; van Loan, Charles, Nineteen dubious ways to compute the exponential of a matrix, SIAM review, Vol. 20, 801-836, (1976) · Zbl 0395.65012
[173] Newbery, A.C.R., Quality tests for linear equation solvers, Department of computer science, university of kentucky, technical report no. 18-75, 20, (1975)
[174] Norin, Robert S., Sparse matrix calculations using an array processor, (), 183-187
[175] Panttaja, James, A comparison of the PLU and QR methods for determining eigenvalues of real Hessenberg matrices, (), 252
[176] Parlett, B.N.; Wang, Y., The influence of the compiler on the cost of mathematical software, (), 35-46 · Zbl 0312.68017
[177] Pereyra, V.; Scherer, Godela, Eigenvalues of symmetric tridiagonal matrices: A fast, accurate and reliable algorithm, Journal of the institute of mathematics and its applications, Vol. 12, 209-222, (1973) · Zbl 0278.65035
[178] de Pillis, John, Faster convergence for iterative solutions to systems via three-part splittings, SIAM journal on numerical analysis, Vol. 15, 888-911, (1978) · Zbl 0407.65016
[179] Redish, K.A.; Ward, W.A., Summary of “eigenvalue and eigenvector routines in the mcmaster program library”, SIGNUM newsletter, Vol. 6, No. 2, 8-9, (1971), May 1971
[180] Reid, J.K., Sparse matrices, (), 85-146 · Zbl 0615.65049
[181] Ruhe, Axel; Kågström, Bo., Numerical computation of matrix functions, (), 634, Abstract in
[182] Sanderson, Jim, A proof of convergence for the tridiagonal QL algorithm in floating-point arithmetic, (), 778, Abstract in
[183] Sherman, Andrew H., On Newton-iterative methods for the solution of systems of nonlinear equations, SIAM journal on numerical analysis, Vol. 15, 755-771, (1978) · Zbl 0396.65019
[184] Sherman, Andrew H., Algorithms for sparse Gaussian elimination with partial pivoting, ACM transactions on mathematical software, Vol. 4, 330-338, (1978) · Zbl 0398.65010
[185] Smith, B.T.; Boyle, J.M.; Dongarra, J.J.; Garbow, B.S.; Ikebe, Y.; Klema, V.C.; Moler, C.B., Matrix eigensystem routines — EISPACK guide, (), 551 · Zbl 0325.65016
[186] Smith, Brian T., Can automated theorem provers be used to evaluate linear algebra software?, (), to be published by
[187] Smith, D.A.; Guipre, Pamela S., Modifications to the forsythe-moler algorithm for solving linear algebraic systems, The computer journal, Vol. 21, 174-177, (1978) · Zbl 0373.65017
[188] Sparks, D.N.; Todd, A.D., A comparison of Fortran subroutines for calculating latent roots and vectors, Journal of the royal statistical society, series C (applied statistics), Vol. 22, 220-225, (1973)
[189] Spiess, J., Investigations of speed-ups by new algorithms for matrix multiplication, Computing, Vol. 17, 23-36, (1976)
[190] Tuttle, P.G.; Brown, R.L., The implementation of selected eigenvalue algorithms on a vector computer, (), 831, Abstract in
[191] Wang, H.H., On some experience using the SSOR and related methods for the numerical solution of diffusion equation, (), 400, Abstract in
[192] Young, David M., Iterative solution of linear systems arising from finite element techniques, (), 439-464
[193] Zielke, Gerhard, Test matrices for generalized inverses, SIGNUM newsletter, Vol. 13, No. 4, 10-12, (1978), December 1978
[194] Björck, Åke, Methods for sparse linear least squares problems, () · Zbl 0351.65004
[195] Björck, Åke, Comment on the iterative refinement of least squares solutions, () · Zbl 0757.65047
[196] Blue, James L., Robust algorithms for solving systems of nonlinear equations, () · Zbl 0465.65028
[197] Boland, W.R.; Kowalik, J.S., Extended conjugate gradient methods, (), 7, No. 4 (December 1977) · Zbl 0416.49019
[198] Brent, R.P., Multiple-precision zero-finding methods and the complexity of elementary function evaluation, (), 151-176
[199] Brent, R.P., A Fortran multiple-precision arithmetic package, ACM transactions on mathematical software, Vol. 4, 57-81, (1978)
[200] Colville, A.R., A comparative study of nonlinear programming codes, () · Zbl 0224.90069
[201] Cosnard, M.; More, J.J., Numerical comparison of nonlinear equation solvers, (), 818, Abstract in
[202] Dennis, J., Non-linear least squares and equations, (), 269-312
[203] Dennis, J.E.; Schnabel, R.B., Least change secant updates for quasi-Newton methods, () · Zbl 0424.65020
[204] Eason, E.D.; Fenton, R.G., A comparison of numerical optimization methods for engineering design, Journal of engineering for industry, trans. A.S.M.E., Vol. 96, No. 1, 196-200, (1974), Series B
[205] Elden, Lars, Algorithms for the regularization of ill-conditioned least squares problems, Bit, Vol. 17, 134-145, (1977) · Zbl 0362.65105
[206] Elfving, Tommy, Some numerical results obtained with two gradient methods for solving the linear least square problems, () · Zbl 0768.65013
[207] Gill, Philip E.; Murray, Walter, Algorithms for the solution of the nonlinear least-squares problem, SIAM journal on numerical analysis, Vol. 15, 977-992, (1978) · Zbl 0401.65042
[208] Greenberg, Harvey J., Design and implementation of optimization software, (), 566
[209] Haskell, K.H.; Hanson, R.J., An algorithm and Fortran code for the linearly constrained least squares problem, (), 13, No. 4 (December 1977)
[210] Hillstrom, Kenneth E., A simulation test approach to the evaluation of nonlinear optimization algorithms, ACM transactions on mathematical software, Vol. 3, 305-315, (1977)
[211] Ida, Tetsuo; Goto, Eiichi, Overflow free and variable precision computing in FLATS, J. information processing, Vol. 1, 140-142, (1978)
[212] Larichev, O.I.; Gorvits, G.G., New approach to comparison of search methods used in nonlinear programming problems, Journal of optimization theory and applications, Vol. 13, 635-659, (1974) · Zbl 0261.90058
[213] Lasdon, L.S.; Waren, A.D.; Jain, A.; Ratner, M., Design and testing of a generalized reduced gradient code for nonlinear programming, ACM transactions on mathematical software, Vol. 4, 34-50, (1978) · Zbl 0378.90080
[214] Lawson, Charles L.; Hanson, Richard J., Solving least squares problems, (), 340 · Zbl 0860.65028
[215] Lyness, J.N., On the nature of benchmark problems for evaluating optimization routines, (), 8, (December 1977)
[216] Mahendrarajah, A.; Fiala, F., A comparison of three algorithms for linear zero-one programs, ACM transactions on mathematical software, Vol. 2, 331-334, (1976) · Zbl 0345.65032
[217] More, J., Software for nonlinear optimization problems, (), 6, (December 1977)
[218] More, Jorge J., Developing and testing quality optimization software, (), to be published by · Zbl 0548.90074
[219] Murray, Walter; Gill, Philip E., Performance evaluation for optimization software, (), to be published by · Zbl 0297.90082
[220] Nerinckx, D.; Haegemans, A., A comparison of non-linear equation solvers, Journal of computational and applied mathematics, Vol. 2, 145-148, (1976) · Zbl 0332.65027
[221] Paige, C.C.; Saunders, M.A., Least squares estimation of discrete linear dynamic systems using orthogonal transformations, SIAM journal on numerical analysis, Vol. 14, 180-193, (1977) · Zbl 0358.93037
[222] Powell, M.J.D., A view of unconstrained minimization algorithms that do not require derivatives, ACM transactions on mathematical software, Vol. 1, 97-107, (1975) · Zbl 0303.65059
[223] Ramsin, Håkan, Metoder och program för ickelinjär optimering, (), in Swedish
[224] Ramsin, Håkan; Wedin, Per-Åke, A comparison of some algorithms for the nonlinear least squares problem, Bit, Vol. 17, 72-90, (1977) · Zbl 0356.65054
[225] Schittkowski, K.; Zimmerman, P., A factorization method for constrained least squares problems with data changes. part 2: numerical tests, comparisons, and ALGOL-codes, ()
[226] Schittkowski, Klaus, Numerical comparison of optimization software using randomly generated test problems, () · Zbl 0399.90089
[227] Schittkowski, K.; Stoer, J., A factorization method for the solution of constrained linear least squares problems allowing subsequent data changes, Numerische Mathematik, Vol. 31, 431-463, (1979) · Zbl 0378.65026
[228] Schmidt, Jochen W.; Hoyer, Wolfgang, Die verfahren vom Brown-brent-typ bei gemischt linearen-nichtlinearen gleichungssystemen, Zamm, Vol. 58, 425-428, (1978) · Zbl 0406.65024
[229] Schnabel, Robert B., Two aspects affecting development, testing, and performance of software for unconstrained optimization, ()
[230] Schultz, Reinhart, Ein abstiegsvefahren fuer approximationsaufgaben in normierten Räumen, Numerische Mathematik, Vol. 31, 77-95, (1978), in German · Zbl 0413.65010
[231] Spedicato, E.; Greenstadt, J., On some classes of variationally derived quasi-Newton methods for systems of nonlinear algebraic equations, Numerische Mathematik, Vol. 29, 363-380, (1978) · Zbl 0365.65033
[232] Swift, A.; Lindfield, G.R., Comparison of a continuation method with Brent’s method for the numerical solution of a single nonlinear equation, The computer journal, Vol. 21, 359-362, (1978) · Zbl 0385.65022
[233] Toint, Ph.L., Some numerical results using a sparse matrix updating formula in unconstrained optimization, Mathematics of computation, Vol. 32, 839-851, (1978) · Zbl 0381.65036
[234] Wampler, R.H., On the accuracy of least squares computer programs, Journal amer. stat. assoc., Vol. 65, 549-565, (1970) · Zbl 0196.22405
[235] Waren, A.D.; Lasdon, L.S., A survey of nonlinear programming software, (), 275-282
[236] Waren, A.D.; Lasdon, L.S., The status of nonlinear programming software, manuscript, () · Zbl 0378.90080
[237] Waterman, R.J., An evaluation and comparison of three nonlinear programming codes, ()
[238] Weiss, Rotraut, A comparative study of multidimensional function optimizers, ()
[239] Amos, D.E.; Daniel, S.L.; Weston, M.K., CDC 6600 subroutines IBESS and JBESS for Bessel functions I(n,x) and J(n,x), x >= 0, n >= 0, ACM transactions on mathematical software, Vol. 3, 76-92, (1977) · Zbl 0348.65017
[240] Brent, R.P., Fast multiple-precision evaluation of elementary functions, Journal of the association for computing machinery, Vol. 23, 242-251, (1976) · Zbl 0324.65018
[241] Clark, N.A.; Cody, W.J.; Hillstrom, K.E.; Thielieker, E.A., Performance statistics for the FORTRAN IV (H) LIBRARY for the IBM SYSTEM/360, SICNUM newsletter, Vol. 2, No. 3, 7, (1967), December 1967
[242] Clenshaw, C.W., Rational approximations for special functions, (), 275-284
[243] Cody, W.J., Performance testing of function subroutines, (), 759-763
[244] Cody, W.J., Software for the elementary functions, (), 171-186
[245] Cody, W.J., The FUNPACK package of special function subroutines, ACM transactions on mathematical software, Vol. 1, 13-25, (1975) · Zbl 0309.65007
[246] Cody, W.J., An overview of software development for special functions, (), 38-48 · Zbl 0317.65007
[247] Cody, W.J., Transportable test programs for elementary functions, (), 15, No. 4
[248] Cody, W.J.; Motley, Rose M.; Fullerton, L.Wayne, The computation of real fractional order Bessel functions of the second kind, ACM transactions on mathematical software, Vol. 3, 232-239, (1977) · Zbl 0363.33004
[249] Cody, W.J., The challenge in numerical software for microcomputers, (), 1-23 · Zbl 0889.65008
[250] Cox, W.M., UNIVAC claims super accurate Fortran math library, SIGNUM newsletter, Vol. 6, No. 3, 9, (1971), November 1971
[251] Fike, C.T., Computer evaluation of mathematical functions, (1968), Prentice Hall New Jersey · Zbl 0205.19301
[252] Fullerton, L.Wayne, Portable special function routines, (), 452-483
[253] Fullerton, L.W., A portable library of mathematical functions, (), 12, No. 4
[254] Gautschi, Walter, Evaluation of the repeated integrals of the coerror function, ACM transactions on mathematical software, Vol. 3, 240-252, (1977) · Zbl 0363.33001
[255] Gautschi, Walter; Slavik, Josef, On the computation of modified Bessel function ratios, Mathematics of computation, Vol. 32, 865-875, (1978) · Zbl 0386.33006
[256] Gustafson, S.-\(, Convergence acceleration on a general class of power series, Computing, Vol. 21, 53-69, (1978\) · Zbl 0403.65002
[257] Hart, J.F., Computer approximations, (), 343
[258] Hillstrom, K.E., Performance statistics for the FORTRAN IV (H) and PL/I (version 5) libraries in IBM OS 360 release 18, ()
[259] Ho, J.C.; Schryer, N.L., Implementation of supplementary elementary functions for the port library, ()
[260] Kahan, W., Hirondo kuki in memoriam, SIGNUM newsletter, Vol. 7, No. 1, 8-10, (1972), April 1972
[261] Kemp, P., Writing the elementary function procedures for the ALGOL68C compiler, (), 127-144
[262] Kuki, H., Mathematical function subprograms for basic system libraries — objectives, constraints and trade-off, (), 187-199
[263] Kuki, H.; Ascoli, J., FORTRAN extended-precision library, IBM systems journal, Vol. 10, 39-61, (1971)
[264] Lozier, D.W., A bit comparison program for algorithm testing, National bureau of standards, Washington, D.C., report 10-449, (1971)
[265] Luke, Yudell L., Mathematical functions and their approximation, (1975), Academic Press New York · Zbl 0318.33001
[266] Newbery, A.C.R.; Leigh, Ann P., Consistency test for elementary functions, (), 419-422
[267] Ng, Edward W., A comparison of computational methods and algorithms for the complex gamma function, ACM transactions on mathematical software, Vol. 1, 56-70, (1975) · Zbl 0311.65013
[268] Ng, E.W., A comparison of computational algorithms and software for the complex error function and related functions, (), 15, No. 4
[269] Paul, George; Wilson, M.Wayne, Should the elementary function library be incorporated into computer instruction sets?, ACM transactions on mathematical software, Vol. 2, 132-142, (1976)
[270] Schonfelder, J.L., Special functions in the NAG library, (), 285-300
[271] Schonfelder, J.L., The production of special function routines for A multi-machine library, Software-practice and experience, Vol. 6, 71-82, (1976) · Zbl 0317.68024
[272] Schonfelder, J.L., The production and testing of special function software in the NAG library, (), 425-451
[273] Turner, L.Richard, Difficulty in sin/cos routine, SIGNUM newsletter, Vol. 4, No. 3, 13, (1969), October 1969
[274] Wallacw, W., ()
[275] Walther, J.S., A unified algorithm for elementary functions, (), 379-385 · Zbl 0279.68032
[276] Wang, J.Y., The evaluation of periodic functions with large input arguments, SIGNUM newsletter, Vol. 13, No. 4, 7-9, (1978), December 1978
[277] Wyatt, W.T.; Lozier, D.W.; Orser, D.J., A portable extended precision arithmetic package and library with Fortran precompiler, ACM transactions on mathematical software, Vol. 2, 209-231, (1976) · Zbl 0329.65031
[278] Blakemore, M.; Evans, G.A.; Hyslop, J., Comparison of some methods for evaluating infinite range oscillatory integrals, Journal of computational physics, Vol. 22, 352-376, (1976) · Zbl 0354.65015
[279] Blue, James L., Automatic numerical quadrature, The Bell system technical journal, Vol. 56, No. 9, 1651-1678, (1977) · Zbl 0391.65002
[280] Casaletto, J.; Pickett, M.; Rice, J., A comparison of some numerical integration programs, SIGNUM newsletter, Vol. 4, No. 3, 30-40, (1969)
[281] Davis, Philip J.; Rabinowitz, Philip, Methods of numerical integration, (), 459 · Zbl 0304.65016
[282] de Boor, Carl, On writing an automatic integration algorithm, (), 201-209
[283] de Boor, Carl, CADRE: an algorithm for numerical quadrature, (), 417-449
[284] de Doncker, E.; Piessens, R., Measurement of quality of quadrature routines, manuscript, (), 11, January 15, 1976
[285] de Doncker, E.; Piessens, R., A bibliography on automatic integration, Journal of computational and applied mathematics, Vol. 2, 273-280, (1976) · Zbl 0336.65012
[286] de Doncker, Elise; Piessens, Robert, Automatic computation of integrals with singular integrand, over a finite or an infinite range, Computing, Vol. 17, 265-279, (1977) · Zbl 0342.65014
[287] de Doncker, Elise, An adaptive extrapolation algorithm for automatic integration, SIGNUM newsletter, Vol. 13, No. 2, 12-18, (1978), (June 1978)
[288] Dixon, Valerie A., Numerical quadrature: a survey of the available algorithms, (), 105-137
[289] Einarsson, Bo, On the calculation of Fourier integrals, (), 1346-1350 · Zbl 0256.65064
[290] Einarsson, Bo, Testing and evaluation of some subroutines for numerical quadrature, (), 149-157
[291] Einarsson, Bo, Use of Richardson extrapolation for the numerical calculation of Fourier transforms, Journal of computational physics, Vol. 21, 365-370, (1976) · Zbl 0326.65078
[292] Fairweather, G.; Keast, P., A comparison of non-adaptive romberg quadrature routines, ()
[293] Fairweather, Graeme; Keast, Pat, An investigation of romberg quadrature, ACM transactions on mathematical software, Vol. 4, 316-322, (1978) · Zbl 0394.65008
[294] Fritsch, F.N., Comparative study of automatic two-dimensional integration routines, 1. measures of comparison, (), 17, November 1973
[295] Gallaher, L.J., Adaptive quadrature and proof of program correctness, () · Zbl 0198.50704
[296] Garribba, S.; Quartapelle, L.; Reina, G., Algorithm 36 — SNIFF: efficient self-tuning algorithm for numerical integration, Computing, Vol. 20, 363-375, (1978) · Zbl 0394.65007
[297] Hausner, Arthur, NL9 — an adaptive routine for numerical quadrature, (), 367-410
[298] Hazlewood, L.J., An alternative strategy for cautious adaptive quadrature, Journal of the institute of mathematics and its applications, Vol. 20, No. 4, 505-518, (1977) · Zbl 0387.65018
[299] Hoover, W.E.; Frame, J.S., Some multidimensional quadrature formulas using partial derivatives, (), 627
[300] Jacobs, F.J., Truncation error and modified romberg extrapolation for the filon-trapezoidal rule, () · Zbl 0301.65008
[301] Jones, R., Results of some quadrature tests, (1973), unpublished
[302] Kahaner, D.K., Comparison of numerical quadrature formulas, (), 229-259
[303] Kahaner, David, Report on the los alamos quadrature workshop, SIGNUM newsletter, Vol. 11, No. 1, 4-26, (1976), May 1976
[304] Keast, Patrick, The evaluation of one-dimensional quadrature routines, () · Zbl 0572.65008
[305] Krogh, F.T.; Snyder, W.V., Preliminary results with a new quadrature subroutine, Jet propulsion laboratory, section 914, computational memorandum no. 363, (1975), Revised April 1975, Pasadena, California
[306] Krogh, F.T.; Snyder, W.V., Comparison of software for numerical quadrature, (), 634
[307] Krogh, Fred T.; Snyder, W.V., Test results with quadrature software 1977, ()
[308] Lyness, J.N., Some interesting quadrature tests, SICNUM newsletter, Vol. 3, No. 2, 1, (1968), July 1968 · Zbl 0343.65007
[309] Lyness, J.N., GAUSS versus ROMBERG, SIGNUM newsletter, Vol. 4, No. 1, 9, (1969), January 1969
[310] Lyness, J.N., Guidelines for automatic quadrature routines, (), 1351-1355 · Zbl 0256.65010
[311] Lyness, J.N., When not to use an automatic quadrature routine, (), 773 · Zbl 0508.65006
[312] Lyness, J.N.; Kaganove, J.J., Comments on the nature of automatic quadrature routines, ACM transactions on mathematical software, Vol. 2, 65-81, (1976) · Zbl 0317.65009
[313] Lyness, J.N.; Kaganove, J.J., A technique for comparing automatic quadrature routines, The computer journal, Vol. 20, 170-177, (1977) · Zbl 0364.65017
[314] Lyness, J.N., Quid, quo, quadrature?, (), 535-560
[315] Malcolm, Michael A.; Simpson, R.Bruce, Local versus global strategies for adaptive quadrature, ACM transactions on mathematical software, Vol. 1, 129-146, (1975) · Zbl 0303.65019
[316] Oliver, J., A doubly-adaptive Clenshaw-Curtis quadrature method, The computer journal, Vol 15, 141-147, (1972) · Zbl 0236.65022
[317] Patterson, T.N.L., Algorithm 468: algorithm for automatic numerical integration over a finite interval, Communications of the ACM, Vol. 16, 694-699, (1973)
[318] Piessens, R., An algorithm for automatic integration, Angewandte informatik, Vol. 15, 399-401, (1973) · Zbl 0263.65029
[319] Piessens, Robert, An automatic routine for the integration of oscillatory functions, ()
[320] Piessens, Robert; de Doncker, Elise, Testing a new one-dimensional quadrature routine, (), (preliminary results) · Zbl 0342.65014
[321] Piessens, R.; de Doncker, E., (), 22
[322] Rice, John R., The algorithm selection problem, (), 65-118
[323] Section 3, The Selection of Quadrature Algorithms, pp. 77-82.
[324] Sasaki, Tateaki, Multidimensional Monte Carlo integration based on factorized approximation functions, SIAM journal on numerical analysis, Vol. 15, 938-952, (1978) · Zbl 0397.65020
[325] Stetter, Hans J.; Ueberhuber, Christoph W., Proposal for population studies in numerical quadrature, Journal of computational and applied mathematics, Vol. 1, 213-215, (1975) · Zbl 0339.65013
[326] Tompa, H., Romberg versus GAUSS, SIGNUM newsletter, Vol. 4, No. 1, 8, (1969), January 1969
[327] Ueberhuber, Christoph W., A program-package for numerical quadrature, (), 399
[328] Anderssen, R.S., Stable procedures for the inversion of Abel’s equation, Journal of the institute of mathematics and its applications, Vol. 17, 329-342, (1976) · Zbl 0328.65065
[329] Atkinson, Kendall E., (), 230
[330] Atkinson, Kendall, An automatic program for linear Fredholm integral equations of the second kind, ACM transactions on mathematical software, Vol. 2, 154-171, (1976) · Zbl 0328.65063
[331] Baker, C.T.H., (), 1034
[332] Baker, Christopher T.H.; Keech, Malcolm S., Stability regions in the numerical treatment of Volterra integral equations, SIAM journal on numerical analysis, Vol. 15, 394-417, (1978) · Zbl 0409.65056
[333] Baker, Christopher T.H.; Keech, Malcolm S., Stability analysis of certain Runge-Kutta procedures for Volterra integral equations, ACM transactions on mathematical software, Vol. 4, 305-315, (1978) · Zbl 0407.65054
[334] Branca, H.W., The nonlinear Volterra equation of Abel’s kind and its numerical treatment, Computing, Vol. 20, 307-324, (1978) · Zbl 0394.65047
[335] Delves, L.M., An automatic Ritz-Galerkin procedure for the numerical solution of linear Fredholm integral equations of the second kind, (), 238
[336] (), 339
[337] de Hoog, Frank; Weiss, Richard, High order methods for a class of Volterra integral equations with weekly singular kernels, SIAM journal on numerical analysis, Vol. 11, 1166-1180, (1974) · Zbl 0292.65067
[338] Miller, G.F., Algorithms for integral equations, (), 139-147
[339] Noble, B., The numerical solution of integral equations, (), 915-966
[340] Sanderson, James G., A numerical comparison of two methods to solve first kind integral equations, (), 437
[341] Smarzewski, R.; Malinowski, H., Numerical solutions of a class of Abel integral equations, Journal of the institute of mathematics and its applications, Vol. 22, 159-170, (1978) · Zbl 0395.65069
[342] Alexander, Roger, Diagonally implicit Runge-Kutta methods for stiff O.D.E.’s, SIAM journal on numerical analysis, Vol. 14, 1006-1021, (1977) · Zbl 0374.65038
[343] Allgower, E.L.; McCormick, S.F., Newton’s method with mesh refinements for numerical solution of nonlinear two-point boundary value problems, Numerische Mathematik, Vol. 29, 237-260, (1978) · Zbl 0352.65048
[344] Barton, D.; Willers, I.M.; Zahar, R.V.M., Taylor series methods for ordinary differential equations — an evaluation, (), 369-390 · Zbl 0221.65132
[345] Bjurel, Gunnar; Dahlquist, Germund; Lindberg, Bengt; Linde, Sven; Oden, Lars, Survey of stiff ordinary differential equations, ()
[346] Brown, R.Leonard, Evaluation of ordinary differential equation software, Bit, Vol. 18, 103-105, (1978)
[347] Bushard, Louis B., Subroutine packages for the numerical solution of stiff ordinary differential equations, (), 172
[348] Byrne, G.D.; Gear, C.W.; Hindmarsh, A.C.; Hull, T.E.; Krogh, F.T.; Shampine, L.F., Panel discussion of quality software for odes, (), 267-285
[349] Byrne, George D., A comparison of two ODE codes: GEAR and EPISODE, (), 41+8, Submitted for publication
[350] BYRNE, George D et al : Comparative test results for two ODE solvers– EPISODE and GEAR, Argonne National Laboratory Report, to appear.
[351] Cash, J.R.; Liem, C.B., On the computational aspects of semi-implicit Runge-Kutta methods, The computer journal, Vol. 21, 363-365, (1978) · Zbl 0385.65033
[352] Danchick, R., Error estimation and stepsize control in maximum polynomial degree Nordsieck-gear methods, (), 6, No. 4
[353] Enright, W.; Bedet, R.; Hall, G.; Hull, T.; Lindberg, B., On the evaluation of numerical methods for initial value problems in ordinary differential equations, (), 296
[354] Enright, W.H.; Hull, T.E.; Lindberg, B., Comparing numerical methods for stiff systems of O.D.E.:s, Bit, Vol. 15, 10-48, (1975) · Zbl 0301.65040
[355] Enright, W.H.; Hull, T.E., Test results on initial value methods for non-stiff ordinary differential equations, SIAM journal on numerical analysis, Vol. 13, 944-961, (1976) · Zbl 0355.65057
[356] Enright, W.H.; Hull, T.E., Comparing numerical methods for the solution of stiff systems of ODEs arising in chemistry, (), 45-66
[357] Enright, W.H., Improving the efficiency of matrix operations in the numerical solution of stiff ordinary differential equations, ACM transactions on mathematical software, Vol. 4, 127-136, (1978) · Zbl 0382.65029
[358] Enright, Wayne H., Using a testing package for the automatic assessment of numerical methods for o.d.e.’s, (), to be published by
[359] Flaherty, Joseph E.; O’Malley, R.E., The numerical solution of boundary value problems for stiff differential equations, Mathematics of computation, Vol. 31, 66-93, (1977) · Zbl 0402.65049
[360] Fox, P.A., DESUB: integration of a first-order system of ordinary differential equations, (), 477-507
[361] Fox, Phyllis, A comparative study of computer programs for integrating differential equations, Communications of the ACM, Vol. 15, 949-951, (1972) · Zbl 0246.65023
[362] Gear, William, (), 253
[363] Gear, C.W., Experience and problems with the software for the automatic solution of ordinary differential equations, (), 211-227
[364] Gladwell, Ian, Testing ordinary differential equation initial value solvers with implications for library routines, () · Zbl 0432.65041
[365] Guderley, Karl G., A unified view of some methods for stiff two-point boundary value problems, SIAM review, Vol. 17, 416-442, (1975) · Zbl 0313.65063
[366] Hill, D.R., On comparing Adams and natural spline multistep formulas, Mathematics of computation, Vol. 29, 741-745, (1975) · Zbl 0308.65048
[367] Hindmarsh, A.C., Note on the startup of ODE solvers, SIGNUM newsletter, Vol. 11, No. 4, 12-13, (1976), December 1976
[368] de Hoog, Frank R.; Weiss, Richard, Difference methods for boundary value problems with a singularity of the first kind, SIAM journal on numerical analysis, Vol. 13, 775-813, (1976) · Zbl 0372.65034
[369] van der Houwen, Peter J.; Verwer, J.G., Comparison of algorithms for systems of o.d.e. is originating from parabolic initial boundary value problems in two dimensions, (), to be published by
[370] Hull, T.E., The development of software for solving ordinary differential equations, (), 55-63 · Zbl 0272.65068
[371] Hull, T.E.; Enright, W.H.; Fellen, B.M.; Sedgwick, A.E.; Hull, T.E.; Enright, W.H.; Fellen, B.M.; Sedgwick, A.E., Errata, SIAM journal on numerical analysis, SIAM journal on numerical analysis, Vol. 11, 681-637, (1974)
[372] Ingram, H.L., A comparison of digital computer programs for the numerical solution of ordinary differential equations, ()
[373] Jackson, K.R.; Enright, W.H.; Hull, T.E., A theoretical criterion for comparing Runge-Kutta formulas, SIAM journal on numerical analysis, Vol. 15, 618-641, (1978) · Zbl 0391.65030
[374] Jain, M.K.; Saldanha, J.S.V., Higher order difference methods for second order two-point boundary-value problems, Journal of computational and applied mathematics, Vol. 4, 199-206, (1978) · Zbl 0383.65052
[375] Jeltsch, Rolf, Multistep methods using higher derivatives and damping at infinity, Mathematics of computation, Vol. 31, 124-138, (1977) · Zbl 0348.65071
[376] Johnson, A.I.; Barney, J.R., Numerical solution of large systems of stiff ordinary differential equations in a modular simulation framework, (), 97-124
[377] Kemp, P., Mathematical software for ordinary differential equations: Chebyshev series methods, (), 289
[378] Krogh, Fred T., Opinions on matters connected with the evaluation of programs and methods for integrating ordinary differential equations, SIGNUM newsletter, Vol. 7, No. 3, 27-48, (1972), October 1972
[379] Krogh, F.T., On testing a subroutine for the numerical solution of ordinary differential equations, Journal of the association for computing machinery, Vol. 20, 545-562, (1973) · Zbl 0292.65039
[380] Krogh, Fred T., (), 6-8, No. 2
[381] Lambert, J.D., The initial value problem for ordinary differential equations, (), 451-500
[382] Lentini, M.; Pereyra, V., An adaptive finite difference solver for nonlinear two-point boundary problems with mild boundary layers, SIAM journal on numerical analysis, Vol. 14, 91-111, (1977) · Zbl 0358.65069
[383] Lindberg, Bengt, Characterization of optimal stepsize sequences for methods for stiff differential equations, SIAM journal on numerical analysis, Vol. 14, 859-887, (1977) · Zbl 0373.65029
[384] Oppelstrup, Jesper, Integrationsmetoder för ordinära differentialekvationer, (), in Swedish · Zbl 0374.65039
[385] O’Shea, Brendan B., Algorithms for the solution of systems of coupled second order ordinary differential equations, Journal of computational and applied mathematics, Vol. 4, 11-17, (1978) · Zbl 0377.65031
[386] Rentrop, P., A Taylor series method for the numerical solution of two-point boundary value problems, Numerische Mathematik, Vol. 31, 359-375, (1979) · Zbl 0421.65051
[387] Russel, Robert D., A comparison of collocation and finite differences for two-point boundary value problems, SIAM journal on numerical analysis, Vol. 14, 19-39, (1977) · Zbl 0359.65075
[388] Sacks-Davis, R., Error estimates for a stiff differential equation procedure, Mathematics of computation, Vol. 31, 939-953, (1977) · Zbl 0377.65029
[389] Scott, M.R.; Watts, H.A., A systematized collection of codes for solving two-point boundary-value problems, (), 197-227
[390] Scott, Melvin R.; Herman, A., Computational solution of linear two-point boundary value problems via orthonormalization, SIAM journal on numerical analysis, Vol. 14, 40-70, (1977) · Zbl 0357.65058
[391] Shampine, L.F.; Gordon, M.K., Computer solution of ordinary differential equations, () · Zbl 0347.65001
[392] Shampine, L.F., The quality of Runge-Kutta formulas, (), 395-396, Abstract in
[393] Shampine, L.F.; Watts, H.A., Global error estimation for ordinary differential equations, ACM transactions on mathematical software, Vol. 2, 172-186, (1976) · Zbl 0328.65041
[394] Shampine, L.F.; Watts, H.A.; Davenport, S.M., Solving nonstiff ordinary differential equations — the state of the art, SIAM review, Vol. 18, 376-411, (1976) · Zbl 0349.65042
[395] Shampine, L.F.; Watts, H.A., The art of writing a Runge-Kutta code, (), 257-275, Part I · Zbl 0407.68036
[396] Shampine, Lawrence F., Stability properties of Adams codes, ACM transactions on mathematical software, Vol. 4, 323-329, (1978) · Zbl 0432.65044
[397] Shampine, L.F.; Gear, C.W., A User’s view of solving stiff ordinary differential equations, SIAM review, Vol. 21, 1-17, (1979) · Zbl 0415.65038
[398] Silver, A.; Sullivan, E., The numerical solution of ordinary differential equations by the Taylor series method, (), 293, Informal Proceedings of a Conference
[399] Sincovec, R.F., On the relative efficiency of higher order collocation methods for solving two-point boundary value problems, SIAM journal on numerical analysis, Vol. 14, 112-123, (1977) · Zbl 0357.65054
[400] Skeel, Robert D.; Kong, Antony K., Blended linear multistep methods, ACM transactions on mathematical software, Vol. 3, 326-345, (1977) · Zbl 0399.65045
[401] Stetter, H.J., On the maximal order in PC-codes, Computing, Vol. 20, 273-280, (1978) · Zbl 0388.65033
[402] Stetter, Hans J., Performance evaluation of o.d.e. software through modelling, (), to be published by
[403] Tendler, Joel M.; Bickart, Theodore A.; Picel, Zdenek, A stiffly stable integration process using cyclic composite methods, ACM transactions on mathematical software, Vol. 4, 339-368, (1978) · Zbl 0409.65034
[404] Thiele, F., Accurate numerical solutions of boundary layer flows by the finite-difference methods of Hermitian type, Journal of computational physics, Vol. 27, 138-159, (1978) · Zbl 0391.76023
[405] Thompson, S.; Bushard, L.D., A comparison of available software for the numerical solution of stiff ordinary differential equations, (), 398, Abstract in
[406] Verner, J.H., Explicit Runge-Kutta methods with estimates of the local truncation error, SIAM journal on numerical analysis, Vol. 15, 772-790, (1978) · Zbl 0403.65029
[407] Walsh, Joan, Initial and boundary value routines for ordinary differential equations, (), 177-189
[408] Walsh, J., Boundary-value problems in ordinary differential equations, (), 501-533
[409] Watanabe, Daniel S., Block implicit one-step methods, Mathematics of computation, Vol. 32, 405-414, (1978) · Zbl 0387.65044
[410] Yu, T., Comparison of numerical methods for ordinary differential equations, ()
[411] Axelsson, Owe, A class of iterative methods for finite element equations, Computer methods in applied mechanics and engineering, Vol. 9, No. 2, 123-137, (1976) · Zbl 0334.65028
[412] Axelsson, Owe; Nävert, Uno, On a graphical package for nonlinear partial differential equation problems, (), 103-108 · Zbl 0376.65042
[413] Banegas, Alexandra, Fast Poisson solvers for problems with sparsity, Mathematics of computation, Vol. 32, 441-446, (1978) · Zbl 0375.65046
[414] Boisvert, R.F.; Houstis, E.N.; Rice, J.R., A system for performance evaluation of partial differential equations software, ()
[415] Buzbee, B.L.; Golub, G.H.; Howell, J.A., Vectorization for the CRAY-1 of some methods for solving elliptic difference equations, (), 255-271
[416] Carver, M.B.; Hinds, H.W., The method of lines and the advective equation, (), 9-10, No. 4
[417] Cash, J.R., High order methods for the numerical integration of ordinary differential equations, Numerische Mathematik, Vol. 30, 385-409, (1978) · Zbl 0369.65019
[418] Chance, M.S.; Greene, J.M.; Grimm, R.C.; Johnson, J.L.; Manickam, J.; Kerner, W.; Berger, D.; Bernard, L.C.; Gruber, R.; Troyon, F., Comparative numerical studies of ideal magnetohydrodynamic instabilities, Journal of computational physics, Vol. 28, 1-13, (1978)
[419] Chandra, R.; Elsenstat, S.C.; Schultz, M.H., Conjugate gradient methods for partial differential equations, (), 60-64, Available from
[420] Chandra, R.; Eisenstat, S.C.; Schultz, M.H., The modified conjugate residual method for partial differential equations, (), 13-19, Available from
[421] Chang, P.W.; Finlayson, B.A., Orthogonal collocation on finite elements for elliptic equations, (), 79-86, Available from · Zbl 0378.65063
[422] Chong, T.H., A variable mesh finite difference method for solving a class of parabolic differential equations in one space variable, SIAM journal on numerical analysis, Vol. 15, 835-857, (1978) · Zbl 0393.65040
[423] Ciment, Melvyn; Leventhal, Stephen H.; Weinberg, Bernhard C., The operator compact implicit method for parabolic equations, Journal of computational physics, Vol. 28, 135-166, (1978) · Zbl 0393.65038
[424] Concus, P.; Golub, G.H.; O’Leary, D.P., Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method, Computing, Vol. 19, 321-339, (1978) · Zbl 0385.65048
[425] Dietrich, D.; McDonald, B.E.; Warn-Varnas, A., Optimized block-implicit relaxation, (), 59, Available from · Zbl 0322.76013
[426] Fröier, Mats, Programsystem för FEM-analys, (), 409-424, (In Swedish)
[427] Gary, John, Comparison of some fourth order difference schemes for hyperbolic problems, (), 14-16, Available from
[428] Girous, E.Dick, A large mathematical model implementation on the STAR-100 computers, (), 287-298
[429] Gottlieb, David; Turkel, Eli, Boundary conditions for multistep finite-difference methods for time-dependent equations, Journal of computational physics, Vol. 26, 181-196, (1978) · Zbl 0388.65039
[430] Grooms, David W., Integration of partial differential equations, ()
[431] Hackbusch, W., On the multi-grid method applied to difference equations, Computing, Vol. 20, 291-306, (1978) · Zbl 0391.65045
[432] Hicks, D.L.; Madsen, M.M., An accuracy property of certain hyperbolic difference schemes, Sandia laboratories, SAND-76-0389, (1976), Albuquerque, New Mexico
[433] Hopkins, T.R.; Wait, R., A comparison of numerical methods for the solution of quasilinear partial differential equations, Computer methods in applied mechanics and engineering, Vol. 9, 181-190, (1976) · Zbl 0334.65068
[434] Houstis, E.N.; Lynch, R.E.; Papatheodorou, T.S.; Rice, J.R., Development, evaluation and selection of methods for partial differential equations, (), 1-6, Available from · Zbl 0302.65075
[435] Houstis, E.N.; Rice, J.R., Software for linear elliptic problems on general two dimensional domains, (), 7-12, Available from
[436] Houstis, E.N.; Papatheodorou, T.S., Comparison of fast direct methods for elliptic problems, (), 46-52, Available from · Zbl 0432.65054
[437] Houstis, E.N.; Lynch, R.E.; Rice, J.R.; Papatheodorou, T.S., Evaluation of numerical methods for elliptic partial differential equations, Journal of computational physics, Vol. 27, 323-350, (1978) · Zbl 0381.65059
[438] Houstis, E.N., Collocation methods for linear elliptic problems, Bit, Vol. 18, 301-310, (1978) · Zbl 0397.65076
[439] Houstis, E.N., The complexity of numerical methods for elliptic partial differential equations, Journal of computational and applied mathematics, Vol. 4, 191-197, (1978) · Zbl 0383.65062
[440] Jezernik, A.; Leech, A., The comparison of iterative and direct solution techniques in the analysis of time-dependent stress problems, including creep, by the finite element method, (), 449-462 · Zbl 0285.73075
[441] Kendall, Richard P.; Wheeler, Mary F., A Crank-Nicolson-H-1-GALERKIN procedure for parabolic problems in a single-space variable, SIAM journal on numerical analysis, Vol. 13, 861-876, (1976) · Zbl 0355.65084
[442] Kincaid, David R.; Young, David M., ITPACK—codes for solving large sparse linear systems by iterative methods: preliminary report, (), 133, Available from
[443] Lawson, J.D.; Morris, J.Ll., The extrapolation of fist order methods for parabolic partial differential equations. I, SIAM journal on numerical analysis, Vol. 15, 1212-1224, (1978) · Zbl 0397.65064
[444] Lynch, Robert E.; Rice, John R., High accuracy finite difference approximation to solutions of elliptic partial differential equations, (), 2541-2544, No. 6 · Zbl 0377.65045
[445] Lynch, R.E.; Rice, J.R., The HODIE method and its performance, (), 143-175
[446] Madsen, Niel K., Numerical results using collocation methods for partial differential equations, (), 389, Abstract in
[447] Madsen, Niel K.; Sincovec, Richard F., General software for partial differential equations, (), 229-242 · Zbl 0311.65057
[448] Majda, Andrew; McDonough, James; Osher, Stanley, The Fourier method for nonsmooth initial data, Mathematics of computation, Vol. 32, 1041-1081, (1978) · Zbl 0393.65039
[449] Melgaard, D.K., PDETWO: general software for two-dimensional partial differential equations, (), 389-390, Abstract in
[450] Ortega, James M.; Voigt, Robert G., Solution of partial differential equations on vector computers, (), 475-525
[451] Polak, S.J.; Schrooten, J.; Binkhuysen, C.; Barneveld, TEDDY2, A program package for parabolic composite region problems, ACM transactions on mathematical software, Vol. 4, 209-227, (1978)
[452] Proskurowski, W., On the numerical solution of the eigenvalue problem of the Laplace operator by a capacitance matrix method, Computing, Vol. 20, 139-151, (1978) · Zbl 0402.65058
[453] Rice, John R., Algorithmic progress in solving partial differential equations, SIGNUM newsletter, Vol. 11, No. 4, 6-10, (1976), (December 1976)
[454] Rice, John R., ELLPACK: A research tool for elliptic partial differential equations software, (), 319-341 · Zbl 0407.68038
[455] Roache, Patrick J., Recent developments and problem areas in computational fluid dynamics, (), 195-256, “Computational Mechanics” · Zbl 0306.76001
[456] Seitelman, L.H., Some practical solution techniques for finite element analysis, (), 471-481 · Zbl 0284.73051
[457] Shieh, A.S.L., Fast Poisson solvers on general two dimensional regions for the Dirichlet problem, Numerische Mathematik, Vol. 31, 405-429, (1979) · Zbl 0431.65064
[458] Sincovec, R.F.; Madsen, N.K., PDECOL: A collocation package for solving partial differential equations, (), 396-397, Abstract in · Zbl 0426.35005
[459] Singh, Kamar J., Improved accuracy of finite element solution by a new reduced integration method, (), 67-73, Available from
[460] Sod, Gary A., A survey of several finite difference-methods for systems of nonlinear hyperbolic conservation laws, Journal of computational physics, Vol. 27, 1-31, (1978) · Zbl 0387.76063
[461] Squire, William; Trapp, George, Solution of partial differential equations by numerical inversion of the Laplace transform, (), 76-79, Available from
[462] Swartz, Blair, Comparing certain classes of difference and finite element methods for a hyperbolic problem, (), 17-19, Available from · Zbl 0302.65082
[463] Tuann, Shin-Yu; Olson, Mervyn D., Review of computing methods for recirculating flows, Journal of computational physics, Vol. 29, 1-19, (1978) · Zbl 0427.76028
[464] Turkel, Eli, Composite methods for hyperbolic equations, SIAM journal on numerical analysis, Vol. 14, 744-759, (1977) · Zbl 0372.65036
[465] Turkel, Eli, Extrapolation methods for dynamic partial differential equations, Numerische Mathematik, Vol. 29, 269-285, (1978) · Zbl 0425.65049
[466] Tyler, L.D., Heuristic analysis of convective finite difference technique, (), 314-334 · Zbl 0233.76152
[467] Wilhelmson, Robert B.; Ericksen, James H., Direct solutions for Poisson’s equation in three dimensions, Journal of computational physics, Vol. 25, 319-331, (1977) · Zbl 0373.65052
[468] Young, David M., Iterative solution of linear and nonlinear systems derived from elliptic partial differential equations, (), 265-296, “Computational Mechanics”
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