LEADER 04991nam 2200697Ia 450 001 9910143178703321 005 20200520144314.0 010 $a9786610541829 010 $a9781280541827 010 $a1280541822 010 $a9780471461678 010 $a0471461679 010 $a9780471249719 010 $a0471249718 035 $a(CKB)111087027112076 035 $a(EBL)210513 035 $a(OCoLC)53720723 035 $a(SSID)ssj0000159929 035 $a(PQKBManifestationID)11159322 035 $a(PQKBTitleCode)TC0000159929 035 $a(PQKBWorkID)10182763 035 $a(PQKB)10794806 035 $a(MiAaPQ)EBC210513 035 $a(Perlego)2760590 035 $a(EXLCZ)99111087027112076 100 $a20020506d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFundamentals of matrix computations /$fDavid S. Watkins 205 $a2nd ed. 210 $aNew York $cWiley-Interscience$dc2002 215 $a1 online resource (635 p.) 225 1 $aPure and applied mathematics 300 $aDescription based upon print version of record. 311 08$a9780471213949 311 08$a0471213942 320 $aIncludes bibliographical references (p. 605-610) and indexes. 327 $aContents; Preface; Acknowledgments; 1 Gaussian Elimination and Its Variants; 1.1 Matrix Multiplication; 1.2 Systems of Linear Equations; 1.3 Triangular Systems; 1.4 Positive Definite Systems; Cholesky Decomposition; 1.5 Banded Positive Definite Systems; 1.6 Sparse Positive Definite Systems; 1.7 Gaussian Elimination and the LU Decomposition; 1.8 Gaussian Elimination with Pivoting; 1.9 Sparse Gaussian Elimination; 2 Sensitivity of Linear Systems; 2.1 Vector and Matrix Norms; 2.2 Condition Numbers; 2.3 Perturbing the Coefficient Matrix; 2.4 A Posteriori Error Analysis Using the Residual 327 $a2.5 Roundoff Errors Backward Stability; 2.6 Propagation of Roundoff Errors; 2.7 Backward Error Analysis of Gaussian Elimination; 2.8 Scaling; 2.9 Componentwise Sensitivity Analysis; 3 The Least Squares Problem; 3.1 The Discrete Least Squares Problem; 3.2 Orthogonal Matrices, Rotators, and Reflectors; 3.3 Solution of the Least Squares Problem; 3.4 The Gram-Schmidt Process; 3.5 Geometric Approach; 3.6 Updating the QR Decomposition; 4 The Singular Value Decomposition; 4.1 Introduction; 4.2 Some Basic Applications of Singular Values; 4.3 The SVD and the Least Squares Problem 327 $a4.4 Sensitivity of the Least Squares Problem5 Eigenvalues and Eigenvectors I; 5.1 Systems of Differential Equations; 5.2 Basic Facts; 5.3 The Power Method and Some Simple Extensions; 5.4 Similarity Transforms; 5.5 Reduction to Hessenberg and Tridiagonal Forms; 5.6 The QR Algorithm; 5.7 Implementation of the QR algorithm; 5.8 Use of the QR Algorithm to Calculate Eigenvectors; 5.9 The SVD Revisited; 6 Eigenvalues and Eigenvectors II; 6.1 Eigenspaces and Invariant Subspaces; 6.2 Subspace Iteration, Simultaneous Iteration, and the QR Algorithm; 6.3 Eigenvalues of Large, Sparse Matrices, I 327 $a6.4 Eigenvalues of Large, Sparse Matrices, II6.5 Sensitivity of Eigenvalues and Eigenvectors; 6.6 Methods for the Symmetric Eigenvalue Problem; 6.7 The Generalized Eigenvalue Problem; 7 Iterative Methods for Linear Systems; 7.1 A Model Problem; 7.2 The Classical Iterative Methods; 7.3 Convergence of Iterative Methods; 7.4 Descent Methods; Steepest Descent; 7.5 Preconditioners; 7.6 The Conjugate-Gradient Method; 7.7 Derivation of the CG Algorithm; 7.8 Convergence of the CG Algorithm; 7.9 Indefinite and Nonsymmetric Problems; Appendix: Some Sources of Software for Matrix Computations 327 $aReferencesIndex; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Index of MATLAB Terms; A; B; C; D; E; F; G; H; I; K; L; M; N; O; P; Q; R; S; T; W; X; Y 330 $aA significantly revised and improved introduction to a critical aspect of scientific computationMatrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights.This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergrad 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aMatrices 606 $aNumerical analysis 615 0$aMatrices. 615 0$aNumerical analysis. 676 $a512.9/434 676 $a512.9434 700 $aWatkins$b David S$0311800 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143178703321 996 $aFundamentals of matrix computations$92149281 997 $aUNINA