Avron, Haim; Druinsky, Alex; Toledo, Sivan Spectral condition-number estimation of large sparse matrices. (English) Zbl 1449.65097 Numer. Linear Algebra Appl. 26, No. 3, e2235, 19 p. (2019). MSC: 65F50 65F10 15A12 65F35 PDFBibTeX XMLCite \textit{H. Avron} et al., Numer. Linear Algebra Appl. 26, No. 3, e2235, 19 p. (2019; Zbl 1449.65097) Full Text: DOI arXiv
Feng, Yuehua; Xiao, Jianwei; Gu, Ming Randomized complete pivoting for solving symmetric indefinite linear systems. (English) Zbl 1404.65013 SIAM J. Matrix Anal. Appl. 39, No. 4, 1616-1641 (2018). MSC: 65F05 15A06 15A23 PDFBibTeX XMLCite \textit{Y. Feng} et al., SIAM J. Matrix Anal. Appl. 39, No. 4, 1616--1641 (2018; Zbl 1404.65013) Full Text: DOI arXiv
Dongarra, Jack; Gates, Mark; Haidar, Azzam; Kurzak, Jakub; Luszczek, Piotr; Tomov, Stanimire; Yamazaki, Ichitaro The singular value decomposition: anatomy of optimizing an algorithm for extreme scale. (English) Zbl 1410.65114 SIAM Rev. 60, No. 4, 808-865 (2018). Reviewer: Wei-Ru Xu (Chengdu) MSC: 65F15 65Y15 15A18 15A23 65Y05 PDFBibTeX XMLCite \textit{J. Dongarra} et al., SIAM Rev. 60, No. 4, 808--865 (2018; Zbl 1410.65114) Full Text: DOI
Gentle, James E. Matrix algebra. Theory, computations and applications in statistics. 2nd edition. (English) Zbl 1386.15002 Springer Texts in Statistics. Cham: Springer (ISBN 978-3-319-64866-8/pbk; 978-3-319-64867-5/ebook). xxix, 648 p. (2017). Reviewer: Frank Uhlig (Auburn) MSC: 15-01 62-01 65-01 PDFBibTeX XMLCite \textit{J. E. Gentle}, Matrix algebra. Theory, computations and applications in statistics. 2nd edition. Cham: Springer (2017; Zbl 1386.15002) Full Text: DOI
Chen, Cheng; Fang, Jianbin; Tang, Tao; Yang, Canqun LU factorization on heterogeneous systems: an energy-efficient approach towards high performance. (English) Zbl 1372.65091 Computing 99, No. 8, 791-811 (2017). MSC: 65F05 15A23 65Y05 65Y10 65Y20 PDFBibTeX XMLCite \textit{C. Chen} et al., Computing 99, No. 8, 791--811 (2017; Zbl 1372.65091) Full Text: DOI
Wang, Wei-Guo; Wei, Yimin Mixed and componentwise condition numbers for matrix decompositions. (English) Zbl 1375.65048 Theor. Comput. Sci. 681, 199-216 (2017). MSC: 65F05 15A23 65F35 PDFBibTeX XMLCite \textit{W.-G. Wang} and \textit{Y. Wei}, Theor. Comput. Sci. 681, 199--216 (2017; Zbl 1375.65048) Full Text: DOI
Harbrecht, Helmut; Peters, Michael; Schneider, Reinhold On the low-rank approximation by the pivoted Cholesky decomposition. (English) Zbl 1244.65042 Appl. Numer. Math. 62, No. 4, 428-440 (2012). Reviewer: R. Militaru (Craiova) MSC: 65F05 15B48 47A10 47B07 PDFBibTeX XMLCite \textit{H. Harbrecht} et al., Appl. Numer. Math. 62, No. 4, 428--440 (2012; Zbl 1244.65042) Full Text: DOI
Liu, Qiaohua Modified Gram-Schmidt-based methods for block downdating the Cholesky factorization. (English) Zbl 1213.65050 J. Comput. Appl. Math. 235, No. 8, 1897-1905 (2011). Reviewer: Daniel Kressner (Lausanne) MSC: 65F05 15B48 15B52 PDFBibTeX XMLCite \textit{Q. Liu}, J. Comput. Appl. Math. 235, No. 8, 1897--1905 (2011; Zbl 1213.65050) Full Text: DOI
Bindel, David; Demmel, James; Kahan, William; Marques, Osni On computing Givens rotations reliably and efficiently. (English) Zbl 1072.65048 ACM Trans. Math. Softw. 28, No. 2, 206-238 (2002). MSC: 65F15 15-04 65Y15 65Y20 PDFBibTeX XMLCite \textit{D. Bindel} et al., ACM Trans. Math. Softw. 28, No. 2, 206--238 (2002; Zbl 1072.65048) Full Text: DOI
Li, Xiaoye S.; Martin, Michael C.; Thompson, Brandon J.; Tung, Teresa; Yoo, Daniel J.; Demmel, James W.; Bailey, David H.; Henry, Greg; Hida, Yozo; Iskandar, Jimmy; Kahan, William; Kang, Suh Y.; Kapur, Anil Design, implementation and testing of extended and mixed precision BLAS. (English) Zbl 1070.65523 ACM Trans. Math. Softw. 28, No. 2, 1512-205 (2002). MSC: 65Fxx 15-04 65Y20 PDFBibTeX XMLCite \textit{X. S. Li} et al., ACM Trans. Math. Softw. 28, No. 2, 1512--205 (2002; Zbl 1070.65523) Full Text: DOI Link
An updated set of basic linear algebra subprograms (BLAS). (English) Zbl 1070.65520 ACM Trans. Math. Softw. 28, No. 2, 135-151 (2002). MSC: 65Fxx 15-04 65Y15 PDFBibTeX XMLCite ACM Trans. Math. Softw. 28, No. 2, 135--151 (2002; Zbl 1070.65520) Full Text: DOI
Hopkins, Tim Remark on algorithm 705: A Fortran-77 software package for solving the Sylvester matrix equation \(AXB^T+ CXD^T= E\). (English) Zbl 1070.65536 ACM Trans. Math. Softw. 28, No. 3, 372-375 (2002). MSC: 65F30 15A24 15-04 65Y15 PDFBibTeX XMLCite \textit{T. Hopkins}, ACM Trans. Math. Softw. 28, No. 3, 372--375 (2002; Zbl 1070.65536) Full Text: DOI
Cullum, Jane K.; Willoughby, Ralph A. Lanczos algorithms for large symmetric eigenvalue computations. Vol. I: Theory. (English) Zbl 1013.65033 Classics in Applied Mathematics. 41. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). xx, 273 p. (2002). Reviewer: Ludwig Elsner (Bielefeld) MSC: 65F15 65-02 15-04 65F50 PDFBibTeX XMLCite \textit{J. K. Cullum} and \textit{R. A. Willoughby}, Lanczos algorithms for large symmetric eigenvalue computations. Vol. I: Theory. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2002; Zbl 1013.65033) Full Text: DOI
Bojanczyk, Adam; Qiao, Sanzheng; Steinhardt, Allan O. Unifying unitary and hyperbolic transformations. (English) Zbl 0970.65042 Linear Algebra Appl. 316, No. 1-3, 183-197 (2000). Reviewer: F.Uhlig (Auburn) MSC: 65F25 15A12 65F15 65F05 15B57 PDFBibTeX XMLCite \textit{A. Bojanczyk} et al., Linear Algebra Appl. 316, No. 1--3, 183--197 (2000; Zbl 0970.65042) Full Text: DOI
Konstantinov, M. M.; Stanislavova, M. O.; Petkov, P. Hr. Perturbation bounds and characterisation of the solution of the associated algebraic Riccati equation. (English) Zbl 0933.15025 Linear Algebra Appl. 285, No. 1-3, 7-31 (1998). Reviewer: L.Rodman (Williamsburg) MSC: 15A24 PDFBibTeX XMLCite \textit{M. M. Konstantinov} et al., Linear Algebra Appl. 285, No. 1--3, 7--31 (1998; Zbl 0933.15025) Full Text: DOI
Molchanov, I. N.; Khimich, A. N.; Chistyakova, T. V. Algorithms and computational features of the LINSYST intelligent software product. (English. Russian original) Zbl 0924.65021 Cybern. Syst. Anal. 34, No. 3, 351-359 (1998); translation from Kibern. Sist. Anal. 1998, No. 3, 40-50 (1998). Reviewer: T.C.Mohan (Madras) MSC: 65F05 65Y15 15-04 PDFBibTeX XMLCite \textit{I. N. Molchanov} et al., Cybern. Syst. Anal. 34, No. 3, 351--359 (1998; Zbl 0924.65021); translaton from Kibern. Sist. Anal. 1998, No. 3, 40--50 (1998); translation from Kibern. Sist. Anal. 1998, No. 3, 40--50 (1998) Full Text: DOI
Lehoucq, R. B.; Sorensen, D. C.; Yang, C. ARPACK user’s guide. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. (English) Zbl 0901.65021 Software - Environments - Tools, 6. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. 142 p. (1998). Reviewer: P.Narain (Bombay) MSC: 65F15 65-02 15-04 PDFBibTeX XMLCite \textit{R. B. Lehoucq} et al., ARPACK user's guide. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. Philadelphia, PA: SIAM (1998; Zbl 0901.65021) Full Text: DOI
Dongarra, Jack J.; Walker, David W. Constructing linear algebra software libraries for high-performance computers. (English) Zbl 0938.65057 Chan, Raymond H. (ed.) et al., Iterative methods in scientific computing. Papers from the winter school on Iterative methods in scientific computing and their applications held in Hong Kong, December 14-20, 1995. Singapore: Springer. 111-167 (1997). MSC: 65Fxx 15-04 65Y15 PDFBibTeX XMLCite \textit{J. J. Dongarra} and \textit{D. W. Walker}, in: Iterative methods in scientific computing. Papers from the winter school on Iterative methods in scientific computing and their applications held in Hong Kong, December 14--20, 1995. Singapore: Springer. 111--167 (1997; Zbl 0938.65057)
Hansen, Per Christian Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. (English) Zbl 0890.65037 SIAM Monographs on Mathematical Modeling and Computation, 4. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. 247 p. (1997). Reviewer: C.W.Groetsch (Cincinnati) MSC: 65F20 65J20 47A50 15A09 65R30 45B05 65-02 PDFBibTeX XMLCite \textit{P. C. Hansen}, Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. Philadelphia, PA: SIAM (1997; Zbl 0890.65037) Full Text: DOI
Gilbert, John R.; Ng, Esmond G.; Peyton, Barry W. Separators and structure prediction in sparse orthogonal factorization. (English) Zbl 0881.15015 Linear Algebra Appl. 262, 83-97 (1997). Reviewer: E.Ellers (Toronto) MSC: 15A23 65F05 65F50 PDFBibTeX XMLCite \textit{J. R. Gilbert} et al., Linear Algebra Appl. 262, 83--97 (1997; Zbl 0881.15015) Full Text: DOI
Korn, C. Falcó; Ullrich, C. P. Fast verification of linear system solutions. (English) Zbl 0900.65074 Alefeld, Götz (ed.) et al., Numerical methods and error bounds. Proceedings of the IMACS-GAMM international symposium, Oldenburg, Germany, July 9–12, 1995. Berlin: Akademie Verlag. Math. Res. 89, 80-106 (1996). MSC: 65F05 65F10 65G30 15-04 PDFBibTeX XMLCite \textit{C. F. Korn} and \textit{C. P. Ullrich}, in: Numerical methods and error bounds. Proceedings of the IMACS-GAMM international symposium, Oldenburg, Germany, July 9--12, 1995. Berlin: Akademie Verlag. 80--106 (1996; Zbl 0900.65074)
Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D. LAPACK user’s guide. 2nd ed. (English) Zbl 0843.65018 Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xix, 325 p. (1995). Reviewer: O.Pastravanu (Iaşi) MSC: 65Fxx 65Yxx 65-01 15-04 68-00 68N20 PDFBibTeX XMLCite \textit{E. Anderson} et al., LAPACK user's guide. 2nd ed. Philadelphia, PA: SIAM (1995; Zbl 0843.65018)
Kaufman, Linda Computing the \(MDM^ T\) decomposition. (English) Zbl 0888.65023 ACM Trans. Math. Softw. 21, No. 4, 476-489 (1995). MSC: 65F05 15A21 65Y20 PDFBibTeX XMLCite \textit{L. Kaufman}, ACM Trans. Math. Softw. 21, No. 4, 476--489 (1995; Zbl 0888.65023) Full Text: DOI Link
Dongarra, Jack Performance of LAPACK. (English) Zbl 0832.65023 Gilbert, John (ed.) et al., Advances in numerical analysis. Vol. III: Large-scale matrix problems and the numerical solution of partial differential equations. Proceedings of the fifth summer school in numerical analysis, held at Lancaster University, Lancaster, UK, July 19-31, 1992. Oxford: Clarendon Press. Oxford Science Publications. 55-67 (1994). MSC: 65Fxx 65Y10 15-04 65Y20 PDFBibTeX XMLCite \textit{J. Dongarra}, in: Advances in numerical analysis. Vol. III: Large-scale matrix problems and the numerical solution of partial differential equations. Proceedings of the fifth summer school in numerical analysis, held at Lancaster University, Lancaster, UK, July 19-31, 1992. Oxford: Clarendon Press. 55--67 (1994; Zbl 0832.65023)
Barrett, Richard; Berry, Michael; Chan, Tony F.; Demmel, James; Donato, June; Dongarra, Jack; Eijkhout, Victor; Pozo, Roldan; Romine, Charles; van der Vorst, Henk Templates for the solution of linear systems: building blocks for iterative methods. (English) Zbl 0814.65030 Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xiii, 112 p. (1993). Reviewer: N.Köckler (Paderborn) MSC: 65F10 65-02 15-04 65F50 65F35 65Y05 68W30 PDFBibTeX XMLCite \textit{R. Barrett} et al., Templates for the solution of linear systems: building blocks for iterative methods. Philadelphia, PA: SIAM (1993; Zbl 0814.65030)
Atkinson, E. Neely Computing \(A^ T A-B^ T B=L^ T DL\) using generalized hyperbolic transformations. (English) Zbl 0797.65015 Linear Algebra Appl. 194, 135-147 (1993). Reviewer: C.Moroşanu (Iaşi) MSC: 65F05 15A23 PDFBibTeX XMLCite \textit{E. N. Atkinson}, Linear Algebra Appl. 194, 135--147 (1993; Zbl 0797.65015) Full Text: DOI
Schweitzer, Paul; Stewart, G. W. The Laurent expansion of pencils that are singular at the origin. (English) Zbl 0813.15008 Linear Algebra Appl. 183, 237-254 (1993). MSC: 15A22 65F30 PDFBibTeX XMLCite \textit{P. Schweitzer} and \textit{G. W. Stewart}, Linear Algebra Appl. 183, 237--254 (1993; Zbl 0813.15008) Full Text: DOI
Anderson, E.; Bai, Z.; Bischof, C. LAPACK users’ guide. (English) Zbl 0755.65028 Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xv, 235 p. (1992). Reviewer: O.Pastravanu (Iaşi) MSC: 65Fxx 65Yxx 65-00 15-04 68-00 68N20 PDFBibTeX XMLCite \textit{E. Anderson} et al., LAPACK users' guide. Philadelphia, PA: SIAM (1992; Zbl 0755.65028)
Poole, George; Neal, Larry Gaussian elimination: When is scaling beneficial! (English) Zbl 0748.65026 Linear Algebra Appl. 162-164, 309-324 (1992). Reviewer: A.Galántai (Miskolc-Egyetemvaros) MSC: 65F05 65F35 15A12 PDFBibTeX XMLCite \textit{G. Poole} and \textit{L. Neal}, Linear Algebra Appl. 162--164, 309--324 (1992; Zbl 0748.65026) Full Text: DOI
Hansen, Per Christian; Chan, Tony F. FORTRAN subroutines for general Toeplitz systems. (English) Zbl 0894.65010 ACM Trans. Math. Softw. 18, No. 3, 256-273 (1992). MSC: 65F05 15-04 65F35 65Y15 PDFBibTeX XMLCite \textit{P. C. Hansen} and \textit{T. F. Chan}, ACM Trans. Math. Softw. 18, No. 3, 256--273 (1992; Zbl 0894.65010) Full Text: DOI Link
Bunse-Gerstner, Angelika; Byers, Ralph; Mehrmann, Volker; Nichols, Nancy K. Numerical computation of an analytic singular value decomposition of a matrix valued function. (English) Zbl 0743.65035 Numer. Math. 60, No. 1, 1-39 (1991). Reviewer: F.Szidarovszky (Tucson) MSC: 65F15 15A60 15A18 PDFBibTeX XMLCite \textit{A. Bunse-Gerstner} et al., Numer. Math. 60, No. 1, 1--39 (1991; Zbl 0743.65035) Full Text: DOI EuDML
Zielke, Gerhard Systems of linear equations and generalized inverses: Foundations and numerical methods. (Lineare Gleichungssysteme und verallgemeinerte Inversen: Grundlagen und numerische Verfahren.) (German) Zbl 0739.65040 Wiss. Z., Martin-Luther-Univ. Halle-Wittenberg, Math.-Naturw. Reihe 40, No. 1, 45-59 (1991). Reviewer: F.Uhlig (Auburn) MSC: 65F20 65-02 65F15 15A09 15A18 65F05 15-02 PDFBibTeX XMLCite \textit{G. Zielke}, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg, Math.-Naturwiss. Reihe 40, No. 1, 45--59 (1991; Zbl 0739.65040)
Köckler, Norbert Numerische Algorithmen in Softwaresystemen unter besonderer Berücksichtigung der NAG-Bibliothek. (Numerical algorithms in software systems under special regard of the NAG library). (German) Zbl 0708.65001 Stuttgart: B.G. Teubner. xiv, 394 S. DM 58.00 (mit Diskette) (1990). Reviewer: W.Govaerts MSC: 65-04 65-02 65Fxx 65Hxx 65K05 65Dxx 65Lxx 65Nxx 65Mxx 15-04 90-04 35-04 12-04 34-04 PDFBibTeX XMLCite \textit{N. Köckler}, Numerische Algorithmen in Softwaresystemen unter besonderer Berücksichtigung der NAG-Bibliothek. (Numerical algorithms in software systems under special regard of the NAG library). Stuttgart: B.G. Teubner (1990; Zbl 0708.65001)
Van Huffel, Sabine Partial singular value decomposition algorithm. (English) Zbl 0721.65016 J. Comput. Appl. Math. 33, No. 1, 105-112 (1990). Reviewer: H.Matthies (Hamburg) MSC: 65F15 15-04 15A18 PDFBibTeX XMLCite \textit{S. Van Huffel}, J. Comput. Appl. Math. 33, No. 1, 105--112 (1990; Zbl 0721.65016) Full Text: DOI
Pan, C.-T. A modification to the LINPACK downdating algorithm. (English) Zbl 0718.65014 BIT 30, No. 4, 707-722 (1990). Reviewer: Shenquan Xie (Xiangtan) MSC: 65F05 15A23 PDFBibTeX XMLCite \textit{C. T. Pan}, BIT 30, No. 4, 707--722 (1990; Zbl 0718.65014) Full Text: DOI
Hoffmann, W. An estimate for the spectral norm of the inverse of a matrix with the Gauss-Jordan algorithm. (English) Zbl 0683.65031 J. Comput. Appl. Math. 27, No. 3, 421-428 (1989). Reviewer: F.Szidarovszky MSC: 65F35 65F05 15A60 PDFBibTeX XMLCite \textit{W. Hoffmann}, J. Comput. Appl. Math. 27, No. 3, 421--428 (1989; Zbl 0683.65031) Full Text: DOI
Hake, J.-Fr.; Homberg, W. Linear algebra software in IBM and CRAY computers. (English) Zbl 0679.65015 J. Comput. Appl. Math. 26, No. 3, 311-325 (1989). Reviewer: V.Arnăutu (Iaşi) MSC: 65Fxx 65Y05 15-04 PDFBibTeX XMLCite \textit{J. Fr. Hake} and \textit{W. Homberg}, J. Comput. Appl. Math. 26, No. 3, 311--325 (1989; Zbl 0679.65015) Full Text: DOI
Dekker, T. J.; Hoffmann, W. Rehabilitation of the Gauss-Jordan algorithm. (English) Zbl 0672.65011 Numer. Math. 54, No. 5, 591-599 (1989). Reviewer: I.Arany MSC: 65F05 65Y05 65G50 15A06 PDFBibTeX XMLCite \textit{T. J. Dekker} and \textit{W. Hoffmann}, Numer. Math. 54, No. 5, 591--599 (1989; Zbl 0672.65011) Full Text: DOI EuDML
Hager, William W. Applied numerical linear algebra. (English) Zbl 0665.65021 Englewood Cliffs, NJ: Prentice Hall. VIII, 424 p. $ 64.40 (1988). Reviewer: K.Hainer MSC: 65Fxx 65-01 65Hxx 65Y05 15-04 PDFBibTeX XMLCite \textit{W. W. Hager}, Applied numerical linear algebra. Englewood Cliffs, NJ: Prentice Hall (1988; Zbl 0665.65021)
Motscha, Matthias Algorithm to compute the complex stability radius. (English) Zbl 0672.65016 Int. J. Control 48, No. 6, 2417-2428 (1988). Reviewer: V.Prepeliţă MSC: 65F15 15A18 PDFBibTeX XMLCite \textit{M. Motscha}, Int. J. Control 48, No. 6, 2417--2428 (1988; Zbl 0672.65016) Full Text: DOI
Beattie, Christopher; Fox, David W. Schur complements and the Weinstein-Aronszajn theory for modified matrix eigenvalue problems. (English) Zbl 0661.15008 Linear Algebra Appl. 108, 37-61 (1988). Reviewer: E.Kreyszig MSC: 15A18 65F15 15A42 49R50 PDFBibTeX XMLCite \textit{C. Beattie} and \textit{D. W. Fox}, Linear Algebra Appl. 108, 37--61 (1988; Zbl 0661.15008) Full Text: DOI
Blum, Edward K. The semantics and complexity of parallel programs for vector computations. I: A case study using Ada. (English) Zbl 0656.68020 BIT 28, No. 3, 530-551 (1988). Reviewer: W.Schönauer MSC: 68Q60 65Y05 68Q05 68N25 15A23 PDFBibTeX XMLCite \textit{E. K. Blum}, BIT 28, No. 3, 530--551 (1988; Zbl 0656.68020) Full Text: DOI
Arbenz, Peter; Gander, Walter; Golub, Gene H. Restricted rank modification of the symmetric eigenvalue problem: Theoretical considerations. (English) Zbl 0652.15004 Linear Algebra Appl. 104, 75-95 (1988). Reviewer: L.Elsner MSC: 15A18 65F15 PDFBibTeX XMLCite \textit{P. Arbenz} et al., Linear Algebra Appl. 104, 75--95 (1988; Zbl 0652.15004) Full Text: DOI
Higham, Nicholas J. Computing a nearest symmetric positive semidefinite matrix. (English) Zbl 0649.65026 Linear Algebra Appl. 103, 103-118 (1988). Reviewer: V.G.Rumchev MSC: 65F30 15A60 15B48 65K05 90C25 PDFBibTeX XMLCite \textit{N. J. Higham}, Linear Algebra Appl. 103, 103--118 (1988; Zbl 0649.65026) Full Text: DOI
Bunch, James R. The weak and strong stability of algorithms in numerical linear algebra. (English) Zbl 0652.65032 Linear Algebra Appl. 88-89, 49-66 (1987). MSC: 65F35 15A12 65G50 PDFBibTeX XMLCite \textit{J. R. Bunch}, Linear Algebra Appl. 88--89, 49--66 (1987; Zbl 0652.65032) Full Text: DOI
Tombs, M. S.; Postlethwaite, I. Truncated balanced realization of a stable non-minimal state-space system. (English) Zbl 0642.93015 Int. J. Control 46, 1319-1330 (1987). Reviewer: N.Osetinski MSC: 93B20 93B40 93C05 15A18 15A24 65F30 93B15 PDFBibTeX XMLCite \textit{M. S. Tombs} and \textit{I. Postlethwaite}, Int. J. Control 46, 1319--1330 (1987; Zbl 0642.93015) Full Text: DOI
Petkov, P. Khr.; Khristov, N. D.; Konstantinov, M. M. On the numerical properties of the Schur approach for solving the matrix Riccati equation. (English) Zbl 0635.65043 Syst. Control Lett. 9, 197-201 (1987). Reviewer: V.Prepeliţă MSC: 65F30 65K10 15A24 93C15 PDFBibTeX XMLCite \textit{P. Khr. Petkov} et al., Syst. Control Lett. 9, 197--201 (1987; Zbl 0635.65043) Full Text: DOI
Byers, Ralph; Nash, Stephen On the singular “vectors” of the Lyapunov operator. (English) Zbl 0633.65042 SIAM J. Algebraic Discrete Methods 8, 59-76 (1987). Reviewer: L.Bakule MSC: 65F30 15A18 15A24 93C15 15A45 65K10 PDFBibTeX XMLCite \textit{R. Byers} and \textit{S. Nash}, SIAM J. Algebraic Discrete Methods 8, 59--76 (1987; Zbl 0633.65042) Full Text: DOI
Van Loan, Charles F. On estimating the condition of eigenvalues and eigenvectors. (English) Zbl 0631.65030 Linear Algebra Appl. 88-89, 715-732 (1987). Reviewer: T.Reginska MSC: 65F15 65F35 15A42 PDFBibTeX XMLCite \textit{C. F. Van Loan}, Linear Algebra Appl. 88--89, 715--732 (1987; Zbl 0631.65030) Full Text: DOI Link
Bischof, Christian; Van Loan, Charles F. The WY representation for products of Householder matrices. (English) Zbl 0628.65033 SIAM J. Sci. Stat. Comput. 8, S1-S13 (1987). Reviewer: I.Imam MSC: 65F25 65F05 15A23 65Y05 PDFBibTeX XMLCite \textit{C. Bischof} and \textit{C. F. Van Loan}, SIAM J. Sci. Stat. Comput. 8, S1--S13 (1987; Zbl 0628.65033) Full Text: DOI Link
Hansen, Per Christian Detection of near-singularity in Cholesky and \(LDL^ T\) factorizations. (English) Zbl 0627.65040 J. Comput. Appl. Math. 19, 293-299 (1987). Reviewer: J.Abaffy MSC: 65F15 65F05 15A23 65F50 PDFBibTeX XMLCite \textit{P. C. Hansen}, J. Comput. Appl. Math. 19, 293--299 (1987; Zbl 0627.65040) Full Text: DOI
Hoffmann, W. Solving linear systems on a vector computer. (English) Zbl 0625.65020 J. Comput. Appl. Math. 18, 353-367 (1987). Reviewer: M.Bernadou MSC: 65F05 65Y05 15A23 PDFBibTeX XMLCite \textit{W. Hoffmann}, J. Comput. Appl. Math. 18, 353--367 (1987; Zbl 0625.65020) Full Text: DOI
Niemeyer, Horst; Wermuth, Edgar Lineare Algebra. Analytische und numerische Behandlung. (German) Zbl 0621.15001 Rechnerorientierte Ingenieurmathematik. Braunschweig/Wiesbaden: Friedr. Vieweg & Sohn. XIII, 375 S.; DM 49.80 (1987). Reviewer: V.Mehrmann MSC: 15-01 00A06 65F05 65F10 65F15 15-04 PDFBibTeX XML
Thomas, P. D.; Brown, R. A. LU decomposition of matrices with augmented dense constraints. (English) Zbl 0616.65033 Int. J. Numer. Methods Eng. 24, 1451-1459 (1987). MSC: 65F05 65F50 15A23 PDFBibTeX XMLCite \textit{P. D. Thomas} and \textit{R. A. Brown}, Int. J. Numer. Methods Eng. 24, 1451--1459 (1987; Zbl 0616.65033) Full Text: DOI
Byers, Ralph Solving the algebraic Riccati equation with the matrix sign function. (English) Zbl 0611.65027 Linear Algebra Appl. 85, 267-279 (1987). Reviewer: S.Mirica MSC: 65F30 15A24 PDFBibTeX XMLCite \textit{R. Byers}, Linear Algebra Appl. 85, 267--279 (1987; Zbl 0611.65027) Full Text: DOI
Birdwell, J. Douglas; Laub, Alan J. Balanced singular values for LQG/LTR design. (English) Zbl 0608.93027 Int. J. Control 45, 939-950 (1987). MSC: 93B40 65F35 93C35 15A09 15A18 15A60 93C05 PDFBibTeX XMLCite \textit{J. D. Birdwell} and \textit{A. J. Laub}, Int. J. Control 45, 939--950 (1987; Zbl 0608.93027) Full Text: DOI
Petkov, P. Hr.; Christov, N. D.; Konstantinov, M. M. Numerical analysis of the reduction of linear systems into orthogonal canonical form. (English) Zbl 0606.93029 Syst. Control Lett. 7, 361-364 (1986). Reviewer: M.Voicu MSC: 93B40 93B10 93C05 65G99 15A21 65F25 PDFBibTeX XMLCite \textit{P. Hr. Petkov} et al., Syst. Control Lett. 7, 361--364 (1986; Zbl 0606.93029) Full Text: DOI
Chu, Moody T. A differential equation approach to the singular value decomposition of bidiagonal matrices. (English) Zbl 0601.15005 Linear Algebra Appl. 80, 71-79 (1986). Reviewer: M.de la Sen MSC: 15A18 15B57 15A21 PDFBibTeX XMLCite \textit{M. T. Chu}, Linear Algebra Appl. 80, 71--79 (1986; Zbl 0601.15005) Full Text: DOI
Oshman, Y.; Bar-Itzhack, I. Y. Square root filtering via covariance and information eigenfactors. (English) Zbl 0599.93060 Automatica 22, 599-604 (1986). MSC: 93E11 62M20 93E25 15A18 60G35 62J10 62L12 65L05 PDFBibTeX XMLCite \textit{Y. Oshman} and \textit{I. Y. Bar-Itzhack}, Automatica 22, 599--604 (1986; Zbl 0599.93060) Full Text: DOI
Caron, R. J.; Gould, N. I. M. Finding a positive semidefinite interval for a parametric matrix. (English) Zbl 0593.15015 Linear Algebra Appl. 76, 19-29 (1986). Reviewer: P.Rudra MSC: 15B48 90C20 PDFBibTeX XMLCite \textit{R. J. Caron} and \textit{N. I. M. Gould}, Linear Algebra Appl. 76, 19--29 (1986; Zbl 0593.15015) Full Text: DOI
Foster, Leslie V. Rank and null space calculations using matrix decomposition without column interchanges. (English) Zbl 0589.65031 Linear Algebra Appl. 74, 47-71 (1986). Reviewer: D.Voukalis MSC: 65F30 15A23 PDFBibTeX XMLCite \textit{L. V. Foster}, Linear Algebra Appl. 74, 47--71 (1986; Zbl 0589.65031) Full Text: DOI
Library of programs ”LINAL” for the solution of problems of linear algebra. Operating information material. (Biblioteka programm ”LINAL” dlya resheniya zadach linejnoj algebry. Operativno-informatsionnyj material). (Russian) Zbl 0615.65035 Novosibirsk: Vychislitel’nyj Tsentr SO AN SSSR. 115 p. R. 0.50 (1985). Reviewer: I.N.Molčanov MSC: 65F05 65F15 15-04 65-02 PDFBibTeX XML
Fröberg, Carl-Erik Numerical mathematics. Theory and computer applications. (Rev. ed. of: Introduction to numerical analysis. 2nd ed. 1969). (English) Zbl 0574.65001 Menlo Park, California etc.: The Benjamin/Cummings Publishing Company, Inc. XI, 436 p. (1985). Reviewer: G.Meinardus MSC: 65-01 41-01 65G50 65Fxx 65Dxx 65K05 65Hxx 65C05 65Bxx 65Lxx 65N30 65R20 15-01 44A10 39A10 33-01 PDFBibTeX XML
Il’in, V. P.; Kuznetsov, Yu. I. Tridiagonal matrices and their applications. (Trekhdiagonal’nye matritsy i ikh prilozheniya). (Russian) Zbl 0571.65021 Moskva: “Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 208 p. R. 1.30 (1985). Reviewer: Petko Hr. Petkov MSC: 65Fxx 65-01 15-01 15A06 15A09 65N22 15A18 15B57 PDFBibTeX XML
Aplevich, J. D. Minimal representations of implicit linear systems. (English) Zbl 0565.93012 Automatica 21, 259-269 (1985). Reviewer: H.D.Fischer MSC: 93B20 93B40 93C05 15A03 34A99 65J10 PDFBibTeX XMLCite \textit{J. D. Aplevich}, Automatica 21, 259--269 (1985; Zbl 0565.93012) Full Text: DOI
Van Loan, Charles F. Computing the CS and the generalized singular value decompositions. (English) Zbl 0548.65020 Numer. Math. 46, 479-491 (1985). MSC: 65F15 65F30 15A18 PDFBibTeX XMLCite \textit{C. F. Van Loan}, Numer. Math. 46, 479--491 (1985; Zbl 0548.65020) Full Text: DOI EuDML
Van Loan, Charles F. A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix. (English) Zbl 0565.65018 Linear Algebra Appl. 61, 233-251 (1984). Reviewer: B.Burrows MSC: 65F15 15A18 15B57 PDFBibTeX XMLCite \textit{C. F. Van Loan}, Linear Algebra Appl. 61, 233--251 (1984; Zbl 0565.65018) Full Text: DOI
Dongarra, J. J.; Gustavson, F. G.; Karp, A. Implementing linear algebra algorithms for dense matrices on a vector pipeline machine. (English) Zbl 0539.65009 SIAM Rev. 26, 91-112 (1984). Reviewer: L.Bakule MSC: 65F05 65F30 68N25 15-04 PDFBibTeX XMLCite \textit{J. J. Dongarra} et al., SIAM Rev. 26, 91--112 (1984; Zbl 0539.65009) Full Text: DOI
Kammler, David W. A perturbation analysis of the intrinsic conditioning of an approximate null vector computed with a SVD. (English) Zbl 0522.65026 J. Comput. Appl. Math. 9, 201-204 (1983). MSC: 65F35 65F15 15A12 PDFBibTeX XMLCite \textit{D. W. Kammler}, J. Comput. Appl. Math. 9, 201--204 (1983; Zbl 0522.65026) Full Text: DOI
Crawford, C. R.; Moon, Yiu Sang Finding a positive definite linear combination of two Hermitian matrices. (English) Zbl 0516.15021 Linear Algebra Appl. 51, 37-48 (1983). MSC: 15B57 65F30 15B48 15A18 65F50 PDFBibTeX XMLCite \textit{C. R. Crawford} and \textit{Y. S. Moon}, Linear Algebra Appl. 51, 37--48 (1983; Zbl 0516.15021) Full Text: DOI
Jain, N. K.; Singhal, K.; Huseyin, K. On roots of functional lambda matrices. (English) Zbl 0504.65015 Comput. Methods Appl. Mech. Eng. 40, 277-292 (1983). MSC: 65F15 15A18 15A54 PDFBibTeX XMLCite \textit{N. K. Jain} et al., Comput. Methods Appl. Mech. Eng. 40, 277--292 (1983; Zbl 0504.65015) Full Text: DOI
Stewart, G. W. Computing the CS decomposition of a partitioned orthonormal matrix. (English) Zbl 0516.65016 Numer. Math. 40, 297-306 (1982). MSC: 65F25 15A23 PDFBibTeX XMLCite \textit{G. W. Stewart}, Numer. Math. 40, 297--306 (1982; Zbl 0516.65016) Full Text: DOI EuDML
Hammarling, S. J. Numerical solution of the stable, non-negative definite Lyapunov equation. (English) Zbl 0492.65017 IMA J. Numer. Anal. 2, 303-323 (1982). MSC: 65F05 65K10 15A23 15A24 49J15 93D05 PDFBibTeX XMLCite \textit{S. J. Hammarling}, IMA J. Numer. Anal. 2, 303--323 (1982; Zbl 0492.65017) Full Text: DOI
Emami-Naeini, A.; van Dooren, P. Computation of zeros of linear multivariable systems. (English) Zbl 0484.93029 Automatica 18, 415-430 (1982). MSC: 93B40 93C05 93C35 93B17 15A21 PDFBibTeX XMLCite \textit{A. Emami-Naeini} and \textit{P. van Dooren}, Automatica 18, 415--430 (1982; Zbl 0484.93029) Full Text: DOI
Bunch, James R. Stable algorithms for solving symmetric and skew-symmetric systems. (English) Zbl 0482.65017 Bull. Aust. Math. Soc. 26, 107-119 (1982). MSC: 65F05 15A23 PDFBibTeX XMLCite \textit{J. R. Bunch}, Bull. Aust. Math. Soc. 26, 107--119 (1982; Zbl 0482.65017) Full Text: DOI
Paige, C. C.; Saunders, M. A. Towards a generalized singular value decomposition. (English) Zbl 0471.65018 SIAM J. Numer. Anal. 18, 398-405 (1981). MSC: 65F15 65F20 15A18 PDFBibTeX XMLCite \textit{C. C. Paige} and \textit{M. A. Saunders}, SIAM J. Numer. Anal. 18, 398--405 (1981; Zbl 0471.65018) Full Text: DOI
Dongarra, J. J.; Bunch, J. R.; Moler, C. B.; Stewart, G. W. LINPACK, users’ guide. 2nd printing. (English) Zbl 0476.68025 Philadelphia: SIAM - Society for Industrial and Applied Mathematics. VIII, 356 p. (not consecutively paged) £10.00; DM 51.00 (1980). MSC: 68N99 68-02 15-04 PDFBibTeX XML
Serbin, Steven M. On factoring a class of complex symmetric matrices without pivoting. (English) Zbl 0463.65016 Math. Comput. 35, 1231-1234 (1980). MSC: 65F05 65F30 15A23 PDFBibTeX XMLCite \textit{S. M. Serbin}, Math. Comput. 35, 1231--1234 (1980; Zbl 0463.65016) Full Text: DOI