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## Rall, Louis B.

Compute Distance To:
 Author ID: rall.louis-b Published as: Rall; Rall, L. B.; Rall, Louis B.
 Documents Indexed: 71 Publications since 1930, including 11 Books Reviewing Activity: 1 Review
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#### Co-Authors

 58 single-authored 3 Corliss, George F. 2 Bohlender, Gerd 2 Reps, Thomas W. 2 Ullrich, Christian P. 2 Wolff von Gudenberg, Jürgen 1 Anselone, Philip M. 1 Caprani, Ole 1 Cuyt, Annie A. M. 1 Gray, Julia H. 1 Madsen, Kaj 1 Nashed, M. Zuhair 1 Wanner, Gerhard
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#### Serials

 3 SIAM Journal on Mathematical Analysis 3 SIAM Review 2 Mathematics of Computation 2 ACM Transactions on Mathematical Software 2 Numerische Mathematik 2 SIAM Journal on Numerical Analysis 2 Reliable Computing 1 Journal of Mathematical Analysis and Applications 1 Mathematics Magazine 1 BIT 1 Journal of Optimization Theory and Applications 1 Numerical Functional Analysis and Optimization 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Journal of Integral Equations 1 SIAM Journal on Scientific and Statistical Computing 1 Aequationes Mathematicae 1 Higher-Order and Symbolic Computation 1 Journal of the Society for Industrial & Applied Mathematics 1 Lecture Notes in Computer Science 1 Nonlinear Analysis. Theory, Methods & Applications
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#### Fields

 49 Numerical analysis (65-XX) 15 Computer science (68-XX) 10 Operator theory (47-XX) 6 Integral equations (45-XX) 4 General and overarching topics; collections (00-XX) 4 Ordinary differential equations (34-XX) 4 Approximations and expansions (41-XX) 2 Measure and integration (28-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH

44 Publications have been cited 812 times in 685 Documents Cited by Year
Annotated bibliography on generalized inverses and applications. Zbl 0346.15001
Nashed, M. Z.; Rall, L. B.
1976
Computational solution of nonlinear operator equations. Zbl 0175.15804
Rall, L. B.
1969
Automatic differentiation: techniques and applications. Zbl 0473.68025
Rall, Louis B.
1981
Convergence of the Newton process to multiple solutions. Zbl 0163.38702
Rall, L. B.
1966
Computational solution of nonlinear operator equations. (Reprint with corr.). Zbl 0476.65033
Rall, Louis B.
1979
Quadratic equations in Banach spaces. Zbl 0193.43902
Rall, L. B.
1962
A note on the convergence of Newton’s method. Zbl 0239.65052
Rall, L. B.
1974
The solution of characteristic value-vector problems by Newton’s method. Zbl 0162.46602
Anselone, P. M.; Rall, L. B.
1968
Perturbation methods for the solution of linear problems. Zbl 0405.65030
Rall, L. B.
1979
A comparison of the existence theorems of Kantorovich and Moore. Zbl 0441.65037
Rall, L. B.
1980
Nonlinear functional analysis and applications. Proceedings of an advanced seminar conducted by the Mathematics Research Center, the University of Wisconsin, Madison, October 12-14, 1970. Zbl 0224.00015
Rall, Louis B. (ed.)
1971
On complementary variational principles. Zbl 0135.32502
Rall, L. B.
1966
Corliss, George F.; Rall, L. B.
1987
Applications of software for automatic differentiation in numerical computation. Zbl 0439.68050
Rall, L. B.
1980
An introduction to automatic differentiation. Zbl 0940.65019
Rall, Louis B.; Corliss, George F.
1996
The arithmetic of differentiation. Zbl 0618.65010
Rall, L. B.
1986
Differentiation in Pascal-SC: Type GRADIENT. Zbl 0564.65010
Rall, L. B.
1984
Convergence of Stirling’s method in Banach spaces. Zbl 0298.65040
Rall, L. B.
1975
Integration of interval functions. Zbl 0461.28007
Caprani, Ole; Madsen, Kaj; Rall, L. B.
1981
Error bounds for iterative solutions of Fredholm integral equations. Zbl 0067.35803
Rall, L. B.
1955
Computational implementation of the multivariate Halley method for solving nonlinear systems of equations. Zbl 0556.65041
Cuyt, Annie A. M.; Rall, L. B.
1985
Pascal-SC. A computer language for scientific computation. Zbl 0626.68004
Bohlender, Gerd; Ullrich, Christian; Wolff von Gudenberg, Jürgen; Rall, Louis B.
1987
Mean value and Taylor forms in interval analysis. Zbl 0516.65039
Rall, L. B.
1983
Integration of interval functions. II: The finite case. Zbl 0497.28011
Rall, L. B.
1982
Global optimization using automatic differentiation and interval iteration. Zbl 0617.65060
Rall, L. B.
1987
Numerical integration and the solution of integral equations by the use of Riemann sums. Zbl 0134.13605
Rall, L. B.
1965
Variational methods for nonlinear integral equations. Zbl 0123.31802
Rall, L. B.
1964
Newton’s method for the characteristic value problem $$Ax = \lambda Bx$$. Zbl 0109.09104
Rall, L. B.
1961
Perspectives on automatic differentiation: fast, present, and future? Zbl 1270.65013
Rall, Louis B.
2006
Point and interval differentiation arithmetics. Zbl 0782.65033
Rall, Louis B.
1991
Differentiation and generation of Taylor coefficients in PASCAL-SC. Zbl 0628.68030
Rall, L. B.
1983
Representations of intervals and optimal error bounds. Zbl 0517.65026
Rall, L. B.
1983
On the uniqueness of solutions of quadratic equations. Zbl 0186.21101
Rall, L. B.
1969
PASCAL-SC. Wirkungsvoll programmieren, kontrolliert rechnen. Zbl 0612.68008
Bohlender, Gerd; Ullrich, Christian; Wolff von Gudenberg, Jürgen; Rall, Louis B.
1986
A theory of interval iteration. Zbl 0458.65043
Rall, L. B.
1981
Error in digital computation. Vol. 1. Proceedings of an advanced seminar conducted by the Mathematics Research Center, United States Army, at the University of Wisconsin, Madison October 5-7, 1964. Zbl 0148.00202
Rall, Louis B. (ed.)
1965
Computational divided differencing and divided-difference arithmetics. Zbl 1040.68148
Reps, Thomas W.; Rall, Louis B.
2003
Algorithmic differencing. Zbl 0990.65031
Rall, Louis B.; Reps, Thomas W.
2001
Improved interval bounds for ranges of functions. Zbl 0596.65027
Rall, L. B.
1986
Application of interval integration to the solution of integral equations. Zbl 0529.65077
Rall, L. B.
1984
Solution of finite systems of equations by interval iteration. Zbl 0486.65036
Rall, L. B.
1982
Resolvent kernels of Green’s function kernels and other finite-rank modifications of Fredholm and Volterra kernels. Zbl 0348.45002
Rall, L. B.
1978
A quadratically convergent iteration method for computing zeros of operators satisfying autonomous differential equations. Zbl 0328.65034
Rall, L. B.
1976
Numerical inversion of a class of large matrices. Zbl 0362.65021
Rall, L. B.
1975
Perspectives on automatic differentiation: fast, present, and future? Zbl 1270.65013
Rall, Louis B.
2006
Computational divided differencing and divided-difference arithmetics. Zbl 1040.68148
Reps, Thomas W.; Rall, Louis B.
2003
Algorithmic differencing. Zbl 0990.65031
Rall, Louis B.; Reps, Thomas W.
2001
An introduction to automatic differentiation. Zbl 0940.65019
Rall, Louis B.; Corliss, George F.
1996
Point and interval differentiation arithmetics. Zbl 0782.65033
Rall, Louis B.
1991
Corliss, George F.; Rall, L. B.
1987
Pascal-SC. A computer language for scientific computation. Zbl 0626.68004
Bohlender, Gerd; Ullrich, Christian; Wolff von Gudenberg, Jürgen; Rall, Louis B.
1987
Global optimization using automatic differentiation and interval iteration. Zbl 0617.65060
Rall, L. B.
1987
The arithmetic of differentiation. Zbl 0618.65010
Rall, L. B.
1986
PASCAL-SC. Wirkungsvoll programmieren, kontrolliert rechnen. Zbl 0612.68008
Bohlender, Gerd; Ullrich, Christian; Wolff von Gudenberg, Jürgen; Rall, Louis B.
1986
Improved interval bounds for ranges of functions. Zbl 0596.65027
Rall, L. B.
1986
Computational implementation of the multivariate Halley method for solving nonlinear systems of equations. Zbl 0556.65041
Cuyt, Annie A. M.; Rall, L. B.
1985
Differentiation in Pascal-SC: Type GRADIENT. Zbl 0564.65010
Rall, L. B.
1984
Application of interval integration to the solution of integral equations. Zbl 0529.65077
Rall, L. B.
1984
Mean value and Taylor forms in interval analysis. Zbl 0516.65039
Rall, L. B.
1983
Differentiation and generation of Taylor coefficients in PASCAL-SC. Zbl 0628.68030
Rall, L. B.
1983
Representations of intervals and optimal error bounds. Zbl 0517.65026
Rall, L. B.
1983
Integration of interval functions. II: The finite case. Zbl 0497.28011
Rall, L. B.
1982
Solution of finite systems of equations by interval iteration. Zbl 0486.65036
Rall, L. B.
1982
Automatic differentiation: techniques and applications. Zbl 0473.68025
Rall, Louis B.
1981
Integration of interval functions. Zbl 0461.28007
Caprani, Ole; Madsen, Kaj; Rall, L. B.
1981
A theory of interval iteration. Zbl 0458.65043
Rall, L. B.
1981
A comparison of the existence theorems of Kantorovich and Moore. Zbl 0441.65037
Rall, L. B.
1980
Applications of software for automatic differentiation in numerical computation. Zbl 0439.68050
Rall, L. B.
1980
Computational solution of nonlinear operator equations. (Reprint with corr.). Zbl 0476.65033
Rall, Louis B.
1979
Perturbation methods for the solution of linear problems. Zbl 0405.65030
Rall, L. B.
1979
Resolvent kernels of Green’s function kernels and other finite-rank modifications of Fredholm and Volterra kernels. Zbl 0348.45002
Rall, L. B.
1978
Annotated bibliography on generalized inverses and applications. Zbl 0346.15001
Nashed, M. Z.; Rall, L. B.
1976
A quadratically convergent iteration method for computing zeros of operators satisfying autonomous differential equations. Zbl 0328.65034
Rall, L. B.
1976
Convergence of Stirling’s method in Banach spaces. Zbl 0298.65040
Rall, L. B.
1975
Numerical inversion of a class of large matrices. Zbl 0362.65021
Rall, L. B.
1975
A note on the convergence of Newton’s method. Zbl 0239.65052
Rall, L. B.
1974
Nonlinear functional analysis and applications. Proceedings of an advanced seminar conducted by the Mathematics Research Center, the University of Wisconsin, Madison, October 12-14, 1970. Zbl 0224.00015
Rall, Louis B. (ed.)
1971
Computational solution of nonlinear operator equations. Zbl 0175.15804
Rall, L. B.
1969
On the uniqueness of solutions of quadratic equations. Zbl 0186.21101
Rall, L. B.
1969
The solution of characteristic value-vector problems by Newton’s method. Zbl 0162.46602
Anselone, P. M.; Rall, L. B.
1968
Convergence of the Newton process to multiple solutions. Zbl 0163.38702
Rall, L. B.
1966
On complementary variational principles. Zbl 0135.32502
Rall, L. B.
1966
Numerical integration and the solution of integral equations by the use of Riemann sums. Zbl 0134.13605
Rall, L. B.
1965
Error in digital computation. Vol. 1. Proceedings of an advanced seminar conducted by the Mathematics Research Center, United States Army, at the University of Wisconsin, Madison October 5-7, 1964. Zbl 0148.00202
Rall, Louis B. (ed.)
1965
Variational methods for nonlinear integral equations. Zbl 0123.31802
Rall, L. B.
1964
Quadratic equations in Banach spaces. Zbl 0193.43902
Rall, L. B.
1962
Newton’s method for the characteristic value problem $$Ax = \lambda Bx$$. Zbl 0109.09104
Rall, L. B.
1961
Error bounds for iterative solutions of Fredholm integral equations. Zbl 0067.35803
Rall, L. B.
1955
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#### Cited by 804 Authors

 28 Argyros, Ioannis Konstantinos 18 Gupta, Dharmendra Kumar 16 Hernández, Miguel Ángel 13 Ezquerro, José Antonio 12 Neta, Beny 12 Rall, Louis B. 10 Gutiérrez, José Manuel 10 Nashed, M. Zuhair 10 Wei, Yimin 10 Yamamoto, Tetsuro 9 Engl, Heinz W. 8 Ma, Jipu 8 Magreñán, Ángel Alberto 8 Wang, Yuwen 7 Cuyt, Annie A. M. 7 Geum, Young Hee 7 Hernández-Verón, Miguel Ángel 7 Kim, Young Ik 7 Parhi, Sanjaya Kumar 7 Rump, Siegfried Michael 7 Wolfe, Michael A. 6 Agarwal, Ravi P. 6 Bücker, H. Martin 6 Fischer, Herbert 6 Kou, Jisheng 6 Rokne, Jon G. 6 Singh, Sukhjit 5 Cordero, Alicia 5 Dobner, Hans-Jürgen 5 Hilout, Saïd 5 Hudzik, Henryk 5 Moore, Ramon E. 5 Romero, Natalia 5 Salanova, M. Amparo 5 Torregrosa Sanchez, Juan Ramón 5 Wang, Xiuhua 4 Alefeld, Götz E. 4 Amat, Sergio P. 4 Arthurs, A. M. 4 Chen, Chin-Yun 4 Chen, Dong 4 Chen, Xiaojun 4 Du, Nailin 4 Freeden, Willi 4 Kalaba, Robert E. 4 Kumar, Abhimanyu 4 Martínez, Eulalia 4 Miel, George J. 4 Parida, Pradip K. 4 Prashanth, Maroju 4 Prenter, Patricia M. 4 Schnurr, Marco 4 Shen, Zuhe 4 Silva, Gilson N. 4 Tesfatsion, Leigh 4 Usmani, Riaz A. 3 Ahues, Mario Paul 3 Barrio, Roberto 3 Bischof, Christian H. 3 Busquier, Sonia 3 Chu, King-Wah Eric 3 Chun, Changbum 3 Corach, Gustavo 3 Corliss, George F. 3 Ding, Hengfei 3 Ding, Jiu 3 Dixon, Laurence C. W. 3 Galántai, Aurél 3 Gu, Chuanqing 3 Halıcıoğlu, Sait 3 Hansen, Eldon Robert 3 Harmanci, Abdullah 3 Izumino, Saichi 3 Jaiswal, Jai Prakash 3 Kalla, Shyam Lal 3 Kelley, Carl T. 3 Komkov, Vadim 3 Kramarz, Luis 3 Liu, Xiaoji 3 Marovt, Janko 3 Mayer, Günter 3 Morgan, Alexander P. 3 Mosić, Dijana 3 Ojika, Takeo 3 Pereira, Antônio Luiz 3 Petras, Knut 3 Ratschek, Helmut 3 Saxena, Ram Kishore 3 Scherzer, Otmar 3 Sommese, Andrew John 3 Stanimirović, Predrag S. 3 Ungor, Burcu 3 Vijesh, V. Antony 3 Wampler, Charles W. II 3 Wexler, Anthony S. 3 Wong, Chi Song 3 Wu, Hebing 2 Abad, Alberto J. 2 Anastassiou, George Angelos 2 Andry, Albert N. jun. ...and 704 more Authors
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#### Cited in 182 Serials

 55 Journal of Computational and Applied Mathematics 54 Applied Mathematics and Computation 43 Journal of Mathematical Analysis and Applications 33 Computing 29 Numerische Mathematik 25 Numerical Functional Analysis and Optimization 22 Computers & Mathematics with Applications 19 Numerical Algorithms 19 Linear Algebra and its Applications 12 Mathematics of Computation 12 International Journal of Computer Mathematics 11 Journal of Optimization Theory and Applications 10 Journal of Computational Physics 10 BIT 10 Journal of Complexity 9 Computer Methods in Applied Mechanics and Engineering 9 Nonlinear Analysis. Theory, Methods & Applications 8 Applied Numerical Mathematics 7 Applied Mathematics Letters 6 Mathematics and Computers in Simulation 6 Reliable Computing 5 Journal of Mathematical Physics 5 Integral Equations and Operator Theory 5 Journal of Integral Equations and Applications 5 Journal of Global Optimization 5 Aequationes Mathematicae 5 Journal of Applied Mathematics and Computing 4 Journal of Approximation Theory 4 Journal of Functional Analysis 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Theoretical Computer Science 4 Acta Mathematica Sinica. English Series 3 Applicable Analysis 3 International Journal of Control 3 International Journal of Engineering Science 3 International Journal for Numerical Methods in Fluids 3 Ukrainian Mathematical Journal 3 Calcolo 3 International Journal for Numerical Methods in Engineering 3 Mathematical and Computer Modelling 3 Science in China. Series A 3 Applied Mathematical Modelling 3 Computational Statistics and Data Analysis 3 Mathematical Programming. Series A. Series B 3 Cybernetics and Systems Analysis 3 Journal of Mathematical Sciences (New York) 3 Optimization Methods & Software 3 Wuhan University Journal of Natural Sciences (WUJNS) 3 Journal of Applied Mathematics 3 International Journal of Computational Methods 3 Bulletin of the American Mathematical Society 3 S$$\vec{\text{e}}$$MA Journal 2 Bulletin of the Australian Mathematical Society 2 Computers and Fluids 2 Computer Physics Communications 2 International Journal of Mathematical Education in Science and Technology 2 Mathematical Biosciences 2 Mathematical Methods in the Applied Sciences 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Aplikace Matematiky 2 Czechoslovak Mathematical Journal 2 Information Sciences 2 Journal of Differential Equations 2 Mathematische Nachrichten 2 Mathematica Slovaca 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Tohoku Mathematical Journal. Second Series 2 Physica D 2 Computational Mechanics 2 Journal of Scientific Computing 2 Japan Journal of Industrial and Applied Mathematics 2 Computers and Mathematics with Applications. Part A 2 Electronic Journal of Differential Equations (EJDE) 2 Abstract and Applied Analysis 2 Soft Computing 2 Discrete Dynamics in Nature and Society 2 Computational Geosciences 2 Journal of Algebra and its Applications 2 Analysis in Theory and Applications 2 BIT. Nordisk Tidskrift for Informationsbehandling 2 Frontiers of Mathematics in China 2 Algorithms 1 Artificial Intelligence 1 Biological Cybernetics 1 The Canadian Journal of Statistics 1 Communications in Algebra 1 Communications in Mathematical Physics 1 Discrete Applied Mathematics 1 Ingenieur-Archiv 1 Inverse Problems 1 Information Processing Letters 1 Journal of Engineering Mathematics 1 Journal of Mathematical Biology 1 Linear and Multilinear Algebra 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Automatica 1 Blätter (Deutsche Gesellschaft für Versicherungsmathematik) 1 Demonstratio Mathematica 1 International Journal of Mathematics and Mathematical Sciences ...and 82 more Serials
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#### Cited in 52 Fields

 471 Numerical analysis (65-XX) 180 Operator theory (47-XX) 51 Ordinary differential equations (34-XX) 51 Integral equations (45-XX) 49 Linear and multilinear algebra; matrix theory (15-XX) 46 Operations research, mathematical programming (90-XX) 38 Computer science (68-XX) 37 Partial differential equations (35-XX) 32 Approximations and expansions (41-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 23 Functional analysis (46-XX) 21 Real functions (26-XX) 20 Mechanics of deformable solids (74-XX) 19 Systems theory; control (93-XX) 17 Fluid mechanics (76-XX) 14 Statistics (62-XX) 13 Functions of a complex variable (30-XX) 10 Biology and other natural sciences (92-XX) 9 Probability theory and stochastic processes (60-XX) 8 Field theory and polynomials (12-XX) 8 Quantum theory (81-XX) 7 Geophysics (86-XX) 6 Special functions (33-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Optics, electromagnetic theory (78-XX) 5 Associative rings and algebras (16-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Differential geometry (53-XX) 4 Mechanics of particles and systems (70-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 General and overarching topics; collections (00-XX) 3 Difference and functional equations (39-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral transforms, operational calculus (44-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Astronomy and astrophysics (85-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Commutative algebra (13-XX) 2 Nonassociative rings and algebras (17-XX) 2 Measure and integration (28-XX) 1 Mathematical logic and foundations (03-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX)