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简介

矩阵计算(英文版•第4版)

矩阵计算(英文版•第4版) 9.3分

资源最后更新于 2020-10-22 15:45:11

作者:[美] Gene H. Golub

出版社:人民邮电出版社

出版日期:2014-01

ISBN:9787115346100

文件格式: pdf

标签: 数学 矩阵 计算 LinearAlgebra Mathematics 计算机科学 线性代数 线性代数矩阵

简介· · · · · ·

本书是数值计算领域的名著,系统介绍了矩阵计算的基本理论和方法。内容包括:矩阵乘法、矩阵分析、线性方程组、正交化和最小二乘法、特征值问题、Lanczos 方法、矩阵函数及专题讨论等。书中的许多算法都有现成的软件包实现,每节后附有习题,并有注释和大量参考文献。新版增加约四分之一内容,反映了近年来矩阵计算领域的飞速发展。

本书可作为高等院校数学系高年级本科生和研究生教材,亦可作为计算数学和工程技术人员参考书。

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目录

1 Matrix Multiplication  1
1.1  Basic Algorithms and Notation  2
1.2  Structure and Efficiency  14
1.3  Block Matrices and Algorithms  22
1.4  Fast Matrix-Vector Products  33
1.5  Vectorization and Locality  43
1.6  Parallel Matrix Multiplication  49
2 Matrix Analysis  63
2.1  Basic Ideas from Linear Algebra  64
2.2  Vector Norms  68
2.3  Matrix Norms  71
2.4  The Singular Value Decomposition  76
2.5  Subspace Metrics  81
2.6  The Sensitivity of Square Systems  87
2.7  Finite Precision Matrix Computations  93
3 General Linear Systems  105
3.1  Triangular Systems  106
3.2  The LU Factorization  111
3.3  Roundoff Error in Gaussian Elimination  122
3.4  Pivoting  125
3.5  Improving and Estimating Accuracy  137
3.6  Parallel LU  144
4 Special Linear Systems  153
4.1  Diagonal Dominance and Symmetry  154
4.2  Positive Definite Systems  159
4.3  Banded Systems  176
4.4  Symmetric Indefinite Systems  186
4.5  Block Tridiagonal Systems  196
4.6  Vandermonde Systems  203
4.7  Classical Methods for Toeplitz Systems  208
4.8  Circulant and Discrete Poisson Systems  219
5 Orthogonalization and Least Squares  233
5.1  Householder and Givens Transformations  234
5.2  The QR Factorization  246
5.3  The Full-Rank Least Squares Problem  260
5.4  Other Orthogonal Factorizations  274
5.5  The Rank-Deficient Least Squares Problem  288
5.6  Square and Underdetermined Systems  298
6 Modified Least Squares Problems and Methods  303
6.1  Weighting and Regularization  304
6.2  Constrained Least Squares  313
6.3  Total Least Squares  320
6.4  Subspace Computations with the SVD  327
6.5  Updating Matrix Factorizations  334
7 Unsymmetric Eigenvalue Problems  347
7.1  Properties and Decompositions  348
7.2  Perturbation Theory  357
7.3  Power Iterations  365
7.4  The Hessenberg and Real Schur Forms  376
7.5  The Practical QR Algorithm  385
7.6  Invariant Subspace Computations  394
7.7  The Generalized Eigenvalue Problem  405
7.8  Hamiltonian and Product Eigenvalue Problems  420
7.9  Pseudospectra  426
8 Symmetric Eigenvalue Problems  439
8.1  Properties and Decompositions  440
8.2  Power Iterations  450
8.3  The Symmetric QR Algorithm  458
8.4  More Methods for Tridiagonal Problems  467
8.5  Jacobi Methods  476
8.6  Computing the SVD  486
8.7  Generalized Eigenvalue Problems with Symmetry  497
9 Functions of Matrices  513
9.1  Eigenvalue Methods  514
9.2  Approximation Methods  522
9.3  The Matrix Exponential  530
9.4  The Sign, Square Root, and Log of a Matrix  536
10 Large Sparse Eigenvalue Problems  545
10.1  The Symmetric Lanczos Process  546
10.2  Lanczos, Quadrature, and Approximation  556
10.3  Practical Lanczos Procedures  562
10.4  Large Sparse SVD Frameworks  571
10.5  Krylov Methods for Unsymmetric Problems  579
10.6  Jacobi-Davidson and Related Methods  589
11 Large Sparse Linear System Problems  597
11.1  Direct Methods  598
11.2  The Classical Iterations  611
11.3  The Conjugate Gradient Method  625
11.4  Other Krylov Methods  639
11.5  Preconditioning  650
11.6  The Multigrid Framework  670
12 Special Topics  681
12.1  Linear Systems with Displacement Structure  681
12.2  Structured-Rank Problems  691
12.3  Kronecker Product Computations  707
12.4  Tensor Unfoldings and Contractions  719
12.5  Tensor Decompositions and Iterations  731
Index  747