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矩阵计算 第4版 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

矩阵计算 第4版 英文
  • （美）戈卢布（GENEH.GULUB），（美）范洛恩（CHARLESF.VANLOAN）著 著
  • 出版社： 北京：人民邮电出版社
  • ISBN：9787115346100
  • 出版时间：2014
  • 标注页数：756页
  • 文件大小：96MB
  • 文件页数：776页
  • 主题词：矩阵－计算方法－英文

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图书目录

1 Matrix Multiplication1

1.1 Basic Algorithms and Notation2

1.2 Structure and Efficiency14

1.3 Block Matrices and Algorithms22

1.4 Fast Matrix-Vector Products33

1.5 Vectorization and Locality43

1.6 Parallel Matrix Multiplication49

2 Matrix Analysis63

2.1 Basic Ideas from Linear Algebra64

2.2 Vector Norms68

2.3 Matrix Norms71

2.4 The Singular Value Decomposition76

2.5 Subspace Metrics81

2.6 The Sensitivity of Square Systems87

2.7 Finite Precision Matrix Computations93

3 General Linear Systems105

3.1 Triangular Systems106

3.2 The LU Factorization111

3.3 Roundoff Error in Gaussian Elimination122

3.4 Pivoting125

3.5 Improving and Estimating Accuracy137

3.6 Parallel LU144

4 Special Linear Systems153

4.1 Diagonal Dominance and Symmetry154

4.2 Positive Definite Systems159

4.3 Banded Systems176

4.4 Symmetric Indefinite Systems186

4.5 Block Tridiagonal Systems196

4.6 Vandermonde Systems203

4.7 Classical Methods for Toeplitz Systems208

4.8 Circulant and Discrete Poisson Systems219

5 Orthogonalization and Least Squares233

5.1 Householder and Givens Transformations234

5.2 The QR Factorization246

5.3 The Full-Rank Least Squares Problem260

5.4 Other Orthogonal Factorizations274

5.5 The Rank-Deficient Least Squares Problem288

5.6 Square and Underdetermined Systems298

6 Modified Least Squares Problems and Methods303

6.1 Weighting and Regularization304

6.2 Constrained Least Squares313

6.3 Total Least Squares320

6.4 Subspace Computations with the SVD327

6.5 Updating Matrix Factorizations334

7 Unsymmetric Eigenvalue Problems347

7.1 Properties and Decompositions348

7.2 Perturbation Theory357

7.3 Power Iterations365

7.4 The Hessenberg and Real Schur Forms376

7.5 The Practical QR Algorithm385

7.6 Invariant Subspace Computations394

7.7 The Generalized Eigenvalue Problem405

7.8 Hamiltonian and Product Eigenvalue Problems420

7.9 Pseudospectra426

8 Symmetric Eigenvalue Problems439

8.1 Properties and Decompositions440

8.2 Power Iterations450

8.3 The Symmetric QR Algorithm458

8.4 More Methods for Tridiagonal Problems467

8.5 Jacobi Methods476

8.6 Computing the SVD486

8.7 Generalized Eigenvalue Problems with Symmetry497

9 Functions of Matrices513

9.1 Eigenvalue Methods514

9.2 Approximation Methods522

9.3 The Matrix Exponential530

9.4 The Sign,Square Root,and Log of a Matrix536

10 Large Sparse Eigenvalue Problems545

10.1 The Symmetric Lanczos Process546

10.2 Lanczos,Quadrature,and Approximation556

10.3 Practical Lanczos Procedures562

10.4 Large Sparse SVD Frameworks571

10.5 Krylov Methods for Unsymmetric Problems579

10.6 Jacobi-Davidson and Related Methods589

11 Large Sparse Linear System Problems597

11.1 Direct Methods598

11.2 The Classical Iterations611

11.3 The Conjugate Gradient Method625

11.4 Other Krylov Methods639

11.5 Preconditioning650

11.6 The Multigrid Framework670

12 Special Topics681

12.1 Linear Systems with Displacement Structure681

12.2 Structured-Rank Problems691

12.3 Kronecker Product Computations707

12.4 Tensor Unfoldings and Contractions719

12.5 Tensor Decompositions and Iterations731

Index747

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