矩阵计算-33-(第3版)-(英文版) 内容简介

本书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*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，每节后还附有习题，并有注释和大量参考文献。 本书可作为高等学校数学系高年级本科生和研究生的教材，亦可作为计算数学和工程技术人员的参考用书。

矩阵计算-33-(第3版)-(英文版) 本书特色

《矩阵计算》一书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*小二乘法、特征值问题、Lanczos方法、矩阵函数及专题讨论等。本书可作为高等学校数学系高年级本科生和研究生的教材。

矩阵计算-33-(第3版)-(英文版) 目录

1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342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803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1234Special Linear Systems4.1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1935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2706Parallel Matrix Computations2756.1Basic Concepts2766.2Matrix Multiplication2926.3Factorizations3007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=A Bx3758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4619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49910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54411Functions of Matrices55511.1Eigenvalue Methods55611.2Approximation Methods56211.3The Matrix Exponential57212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621Index637