矩阵计算(英文版?第4版)

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矩阵计算(英文版?第4版)

矩阵计算(英文版?第4版)

作者:Gene

开 本:大16开

书号ISBN:9787115346100

定价:99.0

出版时间:2014-03-01

出版社:人民邮电出版社

矩阵计算(英文版?第4版) 本书特色

《矩阵计算(英文版?第4版)》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*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。   《矩阵计算(英文版?第4版)》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。

矩阵计算(英文版?第4版) 内容简介

现代矩阵计算奠基人gene h. golub名著,国际上关于数值线性代数方面*权威、*全面的一本专著,被美国加州大学、斯坦福大学、华盛顿大学、芝加哥大学、中国科学院研究生院等众多世界知名学府用作相关课程教材或主要参考书。   书中系统介绍了矩阵计算的基本理论和方法,提及的许多算法都有现成的软件包实现。每节后附有习题,并给出了大量注释和参考文献,有助于读者自学和巩固正文内容。   第4版全新改版,新增了约四分之一内容,包括张量计算、快速变换、并行lu等主题,反映了近年来矩阵计算领域的*新进展。

矩阵计算(英文版?第4版) 目录

1 matrix multiplication 
1.1 basic algorithms and notation 
1.2 structure and efficiency 
1.3 block matrices and algorithms 
1.4 fast matrix-vector products 
1.5 vectorization and locality 
1.6 parallel matrix multiplication 

2 matrix analysis 
2.1 basic ideas from linear algebra 
2.2 vector norms 
2.3 matrix norms 
2.4 the singular value decomposition 
2.5 subspace metrics 
2.6 the sensitivity of square systems 
2.7 finite precision matrix computations 

3 general linear systems 
3.1 triangular systems 
3.2 the lu factorization 
3.3 roundoff error in gaussian elimination 
3.4 pivoting 
3.5 improving and estimating accuracy 
3.6 parallel lu 

4 special linear systems 
4.1 diagonal dominance and symmetry 
4.2 positive definite systems 
4.3 banded systems 
4.4 symmetric indefinite systems 
4.5 block tridiagonal systems 
4.6 vandermonde systems 
4.7 classical methods for toeplitz systems 
4.8 circulant and discrete poisson systems 

5 orthogonalization and least squares 
5.1 householder and givens transformations 
5.2 the qr factorization 
5.3 the full-rank least squares problem 
5.4 other orthogonal factorizations 
5.5 the rank-deficient least squares problem 
5.6 square and underdetermined systems 

6 modified least squares problems and methods 
6.1 weighting and regularization 
6.2 constrained least squares 
6.3 total least squares 
6.4 subspace computations with the svd 
6.5 updating matrix factorizations 

7 unsymmetric eigenvalue problems 
7.1 properties and decompositions 
7.2 perturbation theory 
7.3 power iterations 
7.4 the hessenberg and real schur forms 
7.5 the practical qr algorithm 
7.6 invariant subspace computations 
7.7 the generalized eigenvalue problem 
7.8 hamiltonian and product eigenvalue problems 
7.9 pseudospectra 

8 symmetric eigenvalue problems 
8.1 properties and decompositions 
8.2 power iterations 
8.3 the symmetric qr algorithm 
8.4 more methods for tridiagonal problems 
8.5 jacobi methods 
8.6 computing the svd 
8.7 generalized eigenvalue problems with symmetry 

9 functions of matrices 
9.1 eigenvalue methods 
9.2 approximation methods 
9.3 the matrix exponential 
9.4 the sign, square root, and log of a matrix 

10 large sparse eigenvalue problems 
10.1 the symmetric lanczos process 
10.2 lanczos, quadrature, and approximation 
10.3 practical lanczos procedures 
10.4 large sparse svd frameworks 
10.5 krylov methods for unsymmetric problems 
10.6 jacobi-davidson and related methods 

11 large sparse linear system problems 

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自然科学 数学 代数数论组合理论

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