矩阵理论的经典之作,其被引用次数已经超过23000
书名:Matrix computations 3ed (GH Golub, CF Van Loan)
大小:694页
格式:pdf
目录:
Prefaoe to the Third Edition
Software
Selected References xv
1 Matrix Multiplication Problems
Basic Algorithr and Notation 2
Exploiting Structure 16
Block Matrices and Algorithr 24
Vectorization and Re-Use Issue 34
2Matrix Analysis
Basic Ideas fxom Linear Algebra 48
Vector Norms 52
Matrix Norms 54
Finite Precision Matrix Computations 59
Orthogonllty and the SVD 69
Projections and the CS Decomposition75
The Sensitivity of Square Linear Systems 80
3General Linear Systems
The LU Fqorization 94
Roundoff Analysis of Gaussian Elimination
Pivoting 109
Improving and Estimating Accuracy 123
4 Special Linear Systems
The LDM T and LDL T Faorizations 135
Positive Definite Systems 140
Banded Systems 152
Symmetric Indefinite Systems 161
Block Systems 174
Vandermonde Systems and the EFT 183
Toeplitz and Related Systems 193
5Orthogonalization and Least Squares
Householder and Givens Matrices 208
The QR Factorization 223
The Full Rank LS Problem 236
Other Orthogonal Factorizations 248
The Rank Deficient LS Problem 256
Weighting and Iterative Improvement
Square ad UnderdeVermined Systems
6Parallel Matrix Computations
Basic Concepts 276
Matrix Multiplication
Factorizations 300
7The Unsymmetric Eigenvalue Problem
Properties and Decompositions 310
Perturbation Theory 320
Power Iterations 330
The Hessenberg and Real Schur Forms
The Practical QR Algorithm 352
Invariant Sub,pace Computations 362
The QZ Method for Ax = Bx 375
8The Symmetric Eigenvalue Problem
Propertie and Decompositions
Power Iterations 405
The Symmetric QR Algorithm 414
Jacobi Methods 426
Tridiagonal Methods 439
Computing the SVD 448
Some Generli?ed Eigenvalue Problems 461
9Lanczos Methods
Derivation and Convergence Properties 471
Prattics2 Lanczos Procedures 479
Applications to Ax = b and Least Squares 490
Amoldi and Unsymmetric Lanczos 499
10Iterative Methods for Linear System
The Standard Iterations 509
The Conjugate Gradient Method 520
Preconditioned Conjugate Gradients 532
Other Krylov Subspace Methods 544
11Functions of Matrices
Eigenvalue Methods 556
Approximation Methods 562
The Matrix Exponential 572
12Special Topics
Constrained Least Squares 580
Subset Selection Using the SVD 590
Total Least Squares 595
Computing Subspaces with the SVD 601
Updating Matrix Factorizaions 606
Modified/Structured F, igenproblems 621
Bibliography 637
Index 687