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矩阵计算PDF|Epub|txt|kindle电子书版本网盘下载
- （美）GENE H.GOLUB等著 著
- 出版社： 北京：人民邮电出版社
- ISBN：9787115208804
- 出版时间：2009
- 标注页数：646页
- 文件大小：98MB
- 文件页数：672页
- 主题词：矩阵－计算方法－英文
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图书目录
Matrix Multiplication Problems 11
1 Basic Algorithms and Notation 21
2 Exploiting Structure 161
3 Block Matrices and Algorithms 241
4 Vectorization and Re-Use Issues 341
Matrix Analysis 482
1 Basic Ideas from Linear Algebra 482
2 Vector Norms 522
3 Matrix Norms 542
4 Finite Precision Matrix Computations 592
5 Orthogonality and the SVD 692
6 Projections and the CS Decomposition 752
7 The Sensitivity of Square Linear Systems 802
General Linear Systems 873
1 Triangular Systems 883
2 The LU Factorization 943
3 Roundoff Analysis of Gaussian Elimination 1043
4 Pivoting 1093
5 Improving and Estimating Accuracy 1233
Special Linear Systems 1334
1 The LDMT and LDLT Factorizations 1354
2 Positive Definite Systems 1404
3 Banded Systems 1524
4 Symmetric Indefinite Systems 1614
5 Block Systems 1744
6 Vandermonde Systems and the FFT 1834
7 Toeplitz and Related Systems 1934
Orthogonalization and Least Squares 2065
1 Householder and Givens Matrices 2085
2 The QR Factorization 2235
3 The Full Rank LS Problem 2365
4 Other Orthogonal Factorizations 2485
5 The Rank Deficient LS Problem 2565
6 Weighting and Iterative Improvement 2645
7 Square and Underdetermined Systems 2705
Parallel Matrix Computations 2756
1 Basic Concepts 2766
2 Matrix Multiplication 2926
3 Factorizations 3006
The Unsymmetric Eigenvalue Problem 3087
1 Properties and Decompositions 3107
2 Perturbation Theory 3207
3 Power Iterations 3307
4 The Hessenberg and Real Schur Forms 3417
5 The Practical QR Algorithm 3527
6 Invariant Subspace Computations 3627
7 The QZ Method for Ax=λBx 3757
The Symmetric Eigenvalue Problem 3918
1 Properties and Decompositions 3938
2 Power Iterations 4058
3 The Symmetric QR Algorithm 4148
4 Jacobi Methods 4268
5 Tridiagonal Methods 4398
6 Computing the SVD 4488
7 Some Generalized Eigenvalue Problems 4618
Lanczos Methods 4709
1 Derivation and Convergence Properties 4719
2 Practical Lanczos Procedures 4799
3 Applications to Ax=b and Least Squares 4909
4 Arnoldi and Unsymmetric Lanczos 4999
Iterative Methods for Linear Systems 50810
1 The Standard Iterations 50910
2 The Conjugate Gradient Method 52010
3 Preconditioned Conjugate Gradients 53210
4 Other Krylov Subspace Methods 54410
Functions of Matrices 55511
1 Eigenvalue Methods 55611
2 Approximation Methods 56211
3 The Matrix Exponential 57211
Special Topics 57912
1 Constrained Least Squares 58012
2 Subset Selection Using the SVD 59012
3 Total Least Squares 59512
4 Computing Subspaces with the SVD 60112
5 Updating Matrix Factorizations 60612
6 Modified/Structured Eigenproblems 62112