Matrix computations / Gene H. Golub, Charles F. Van Loan.
Series Johns Hopkins series in the mathematical sciences ; 3Editor: Baltimore, Maryland : Johns Hopkins University Press, c1983Descripción: xvi, 476 p. : il. ; 23 cmISBN: 0801830109; 0801830117 (pbk.)Tema(s): Matrices -- Data processingOtra clasificación: 65Fxx (65-02)Preface xi Using the Book XV 1 Background Matrix Algebra [1] 1.1 Vectors and Matrices [1] 1.2 Independence, Orthogonality, Subspaces [4] 1.3 Special Matrices [6] 1.4 Block Matrices and Complex Matrices [8] 2 Measuring Vectors, Matrices, Subspaces, and Linear System Sensitivity [11] 2.1 Vector Norms [12] 2.2 Matrix Norms [14] 2.3 The Singular Value Decomposition [16] 2.4 Orthogonal Projections and the C~S Decomposition [20] 2.5 The Sensitivity of Square Linear Systems [24] 3 Numerical Matrix Algebra [30] 3.1 Matrix Algorithms [30] 3.2 Rounding Errors [32] 3.3 Householder Transformations [38] 3.4 Givens Transformations [43] 3.5 Gauss Transformations [47] 4 Gaussian Elimination [52] 4.1 Triangular Systems [52] 4.2 Computing the L-U Decomposition [54] 4.3 Roundoff Error Analysis of Gaussian Elimination [60] 4.4 Pivoting [64] 4.5 Improving and Estimating Accuracy [71] 5 Special Linear Systems [81] 5.1 The L-D-Mt and L-D-LT Decompositions [82] 5.2 Positive Definite Systems [86] 5.3 Banded Systems [92] 5.4 Symmetric Indefinite Systems [100] 5.5 Block Tridiagonal Systems [110] 5.6 Vandermonde Systems [119] 5.7 Toeplitz Systems [125] 6 Orthogonalization and Least Squares Methods [136] 6.1 Mathematical Properties of the Least Squares Problem [137] 6.2 Householder and Gram-Schmidt Methods [146] 6.3 Givens and Fast Givens Methods [156] 6.4 Rank Deficiency I: QR with Column Pivoting [162] 6.5 Rank Deficiency II: The Singular Value Decomposition [169] 6.6 Weighting and Iterative Improvement [179] 6.7 A Note on Square and Underdetermined Systems [185] 7 The Unsymmetric Eigenvalue Problem [189] 7.1 Properties and Decompositions [190] 7.2 Perturbation Theory [199] 7.3 Power Iterations [208] 7.4 The Hessenberg and Real Schur Decompositions [219] 7.5 The Practical QR Algorithm [228] 7.6 Computing Eigenvectors and Invariant Subspaces' [238] 7.7 The QZ Algorithm and the Ax = λBx Problem [251] 8 The Symmetric Eigenvalue Problem [267] 8.1 Properties, Decompositions, Perturbation Theory [268] 8.2 Tridiagonalization and the Symmetric QR Algorithm [276] 8.3 Once Again: The Singular Value Decomposition [285] 8.4 Jacobi Methods [295] 8.5 Some Special Methods [305] 8.6 More Generalized Eigenvalue Problems [313] 9 Lanczos Methods [322] 9.1 Derivation and Convergence Properties [322] 9.2 Practical Lanczos Procedures [332] 9.3 Applications to Linear Equations and Least Squares [342] 10 Iterative Methods for Linear Systems [352] 10.1 The Standard Iterations [353] 10.2 Derivation and Properties of the Conjugate Gradient Method [362] 10.3 Practical Conjugate Gradient Procedures [372] 11 Functions of Matrices [380] 11.1 Eigenvalue Methods [380] 11.2 Approximation Methods [387] 11.3 The Matrix Exponential [396] 12 Special Topics [404] 12.1 Some Constrained Least Squares Problems [405] 12.2 Subset Selection Using the Singular Value Decomposition [414] 12.3 Total Least Squares [420] 12.4 Comparing Subspaces Using the Singular Value Decomposition [425] 12.5 Some Modified Eigenvalue Problems [431] 12.6 Updating the Q-R Factorization [437] Bibliography [445] Index [469]
| Item type | Home library | Shelving location | Call number | Materials specified | Copy number | Status | Date due | Barcode | Course reserves |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 65 G629 (Browse shelf) | Available | A-5740 | ||||
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 65 G629 (Browse shelf) | Ej. 2 | Available | A-6536 |
Bibliografía: p. 445-468.
Preface xi --
Using the Book XV --
1 Background Matrix Algebra [1] --
1.1 Vectors and Matrices [1] --
1.2 Independence, Orthogonality, Subspaces [4] --
1.3 Special Matrices [6] --
1.4 Block Matrices and Complex Matrices [8] --
2 Measuring Vectors, Matrices, Subspaces, and Linear System Sensitivity [11] --
2.1 Vector Norms [12] --
2.2 Matrix Norms [14] --
2.3 The Singular Value Decomposition [16] --
2.4 Orthogonal Projections and the C~S Decomposition [20] --
2.5 The Sensitivity of Square Linear Systems [24] --
3 Numerical Matrix Algebra [30] --
3.1 Matrix Algorithms [30] --
3.2 Rounding Errors [32] --
3.3 Householder Transformations [38] --
3.4 Givens Transformations [43] --
3.5 Gauss Transformations [47] --
4 Gaussian Elimination [52] --
4.1 Triangular Systems [52] --
4.2 Computing the L-U Decomposition [54] --
4.3 Roundoff Error Analysis of Gaussian Elimination [60] --
4.4 Pivoting [64] --
4.5 Improving and Estimating Accuracy [71] --
5 Special Linear Systems [81] --
5.1 The L-D-Mt and L-D-LT Decompositions [82] --
5.2 Positive Definite Systems [86] --
5.3 Banded Systems [92] --
5.4 Symmetric Indefinite Systems [100] --
5.5 Block Tridiagonal Systems [110] --
5.6 Vandermonde Systems [119] --
5.7 Toeplitz Systems [125] --
6 Orthogonalization and Least Squares Methods [136] --
6.1 Mathematical Properties of the Least Squares Problem [137] --
6.2 Householder and Gram-Schmidt Methods [146] --
6.3 Givens and Fast Givens Methods [156] --
6.4 Rank Deficiency I: QR with Column Pivoting [162] --
6.5 Rank Deficiency II: The Singular Value Decomposition [169] --
6.6 Weighting and Iterative Improvement [179] --
6.7 A Note on Square and Underdetermined Systems [185] --
7 The Unsymmetric Eigenvalue Problem [189] --
7.1 Properties and Decompositions [190] --
7.2 Perturbation Theory [199] --
7.3 Power Iterations [208] --
7.4 The Hessenberg and Real Schur Decompositions [219] --
7.5 The Practical QR Algorithm [228] --
7.6 Computing Eigenvectors and Invariant Subspaces' [238] --
7.7 The QZ Algorithm and the Ax = λBx Problem [251] --
8 The Symmetric Eigenvalue Problem [267] --
8.1 Properties, Decompositions, Perturbation Theory [268] --
8.2 Tridiagonalization and the Symmetric QR Algorithm [276] --
8.3 Once Again: The Singular Value Decomposition [285] --
8.4 Jacobi Methods [295] --
8.5 Some Special Methods [305] --
8.6 More Generalized Eigenvalue Problems [313] --
9 Lanczos Methods [322] --
9.1 Derivation and Convergence Properties [322] --
9.2 Practical Lanczos Procedures [332] --
9.3 Applications to Linear Equations and Least Squares [342] --
10 Iterative Methods for Linear Systems [352] --
10.1 The Standard Iterations [353] --
10.2 Derivation and Properties of the Conjugate Gradient Method [362] --
10.3 Practical Conjugate Gradient Procedures [372] --
11 Functions of Matrices [380] --
11.1 Eigenvalue Methods [380] --
11.2 Approximation Methods [387] --
11.3 The Matrix Exponential [396] --
12 Special Topics [404] --
12.1 Some Constrained Least Squares Problems [405] --
12.2 Subset Selection Using the Singular Value Decomposition [414] --
12.3 Total Least Squares [420] --
12.4 Comparing Subspaces Using the Singular Value Decomposition [425] --
12.5 Some Modified Eigenvalue Problems [431] --
12.6 Updating the Q-R Factorization [437] --
Bibliography [445] --
Index [469] --
MR, 85h:65063
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