- 作 者：（美）GENE H.GOLUB等著
- 出 版 社：北京：人民邮电出版社
- 出版年份：2009
- ISBN：9787115208804
- 标注页数：646 页
- PDF页数：672 页
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Matrix Multiplication Problems 1 1
1 Basic Algorithms and Notation 2 1
2 Exploiting Structure 16 1
3 Block Matrices and Algorithms 24 1
4 Vectorization and Re-Use Issues 34 1
Matrix Analysis 48 2
1 Basic Ideas from Linear Algebra 48 2
2 Vector Norms 52 2
3 Matrix Norms 54 2
4 Finite Precision Matrix Computations 59 2
5 Orthogonality and the SVD 69 2
6 Projections and the CS Decomposition 75 2
7 The Sensitivity of Square Linear Systems 80 2
General Linear Systems 87 3
1 Triangular Systems 88 3
2 The LU Factorization 94 3
3 Roundoff Analysis of Gaussian Elimination 104 3
4 Pivoting 109 3
5 Improving and Estimating Accuracy 123 3
Special Linear Systems 133 4
1 The LDMT and LDLT Factorizations 135 4
2 Positive Definite Systems 140 4
3 Banded Systems 152 4
4 Symmetric Indefinite Systems 161 4
5 Block Systems 174 4
6 Vandermonde Systems and the FFT 183 4
7 Toeplitz and Related Systems 193 4
Orthogonalization and Least Squares 206 5
1 Householder and Givens Matrices 208 5
2 The QR Factorization 223 5
3 The Full Rank LS Problem 236 5
4 Other Orthogonal Factorizations 248 5
5 The Rank Deficient LS Problem 256 5
6 Weighting and Iterative Improvement 264 5
7 Square and Underdetermined Systems 270 5
Parallel Matrix Computations 275 6
1 Basic Concepts 276 6
2 Matrix Multiplication 292 6
3 Factorizations 300 6
The Unsymmetric Eigenvalue Problem 308 7
1 Properties and Decompositions 310 7
2 Perturbation Theory 320 7
3 Power Iterations 330 7
4 The Hessenberg and Real Schur Forms 341 7
5 The Practical QR Algorithm 352 7
6 Invariant Subspace Computations 362 7
7 The QZ Method for Ax=λBx 375 7
The Symmetric Eigenvalue Problem 391 8
1 Properties and Decompositions 393 8
2 Power Iterations 405 8
3 The Symmetric QR Algorithm 414 8
4 Jacobi Methods 426 8
5 Tridiagonal Methods 439 8
6 Computing the SVD 448 8
7 Some Generalized Eigenvalue Problems 461 8
Lanczos Methods 470 9
1 Derivation and Convergence Properties 471 9
2 Practical Lanczos Procedures 479 9
3 Applications to Ax=b and Least Squares 490 9
4 Arnoldi and Unsymmetric Lanczos 499 9
Iterative Methods for Linear Systems 508 10
1 The Standard Iterations 509 10
2 The Conjugate Gradient Method 520 10
3 Preconditioned Conjugate Gradients 532 10
4 Other Krylov Subspace Methods 544 10
Functions of Matrices 555 11
1 Eigenvalue Methods 556 11
2 Approximation Methods 562 11
3 The Matrix Exponential 572 11
Special Topics 579 12
1 Constrained Least Squares 580 12
2 Subset Selection Using the SVD 590 12
3 Total Least Squares 595 12
4 Computing Subspaces with the SVD 601 12
5 Updating Matrix Factorizations 606 12
6 Modified/Structured Eigenproblems 621 12