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金小庆,黄锡荣 著
出版社: 高等教育出版社 ISBN:9787040449945 版次:1 商品编码:11909197 包装:精装 丛书名: 现代应用数学丛书 外文名称:An Introduction to Applied Matrix Analys 开本:16开 出版时间:2016-04-01 用纸:胶版纸 页数:130
黄锡荣,博士,为澳门大学数学系副教授,他的研究领域为偏微分方程解析和数值解。
1. Introduction and Review
1.1 Basic symbols
1.2 Quadratic forms and positive definite matrices
1.2.1 Quadratic forms
1.2.2 Problems involving quadratic forms
1.2.3 Positive definite matrix
1.2.4 Other methods to determine the positive definiteness
1.3 Theorems for eigenvalues of symmetric matrices
1.4 Complex inner product spaces
1.5 Hermitian, unitary, and normal matrices
1.6 Kronecker product and Kronecker sum
2. Norms and Perturbation Analysis
2.1 Vector norms
2.2 Matrix norms
2.3 Perturbation analysis for linear systems
2.4 Error on floating point numbers
3. Least Squares Problems
3.1 Solution of LS problems
3.2 Perturbation analysis for LS problems
3.3 Orthogonal transformations
3.3.1 Householder reflections
3.3.2 Givens rotations
3.4 An algorithm based on QR factorization
3.4.1 QR factorization
3.4.2 A practical algorithm for LS problems
4. Generalized Inverses
4.1 Moore-Penrose generalized inverse
4.2 Basic properties
4.3 Relation to LS problems
4.4 Other generalized inverses
5. Conjugate Gradient Method
5.1 Steepest descent method
5.1.1 Steepest descent method
5.1.2 Convergence rate
5.2 Conjugate gradientmethod
5.2.1 Conjugate gradient method
5.2.2 Basic properties
5.2.3 Practical CG method
5.3 Preconditioning technique
6. Optimal and Superoptimal Preconditioners
6.1 Introduction to optimal preconditioner
6.1.1 Circulantmatrix
6.1.2 Optimal preconditioner
6.2 Linear operator c_U
6.2.1 Algebraic properties
6.2.2 Geometric properties
6.3 Stability
6.4 Superoptimal preconditioner
6.5 Spectral relation of preconditioned matrices
7. Optimal Preconditioners for Functions of Matrices
7.1 Optimal preconditioners for matrix exponential
7.2 Optimal preconditioners for matrix cosine and matrix sine
7.3 Optimal preconditioners for matrix logarithm
8. B?ttcher-Wenzel Conjecture and Related Problems
8.1 Introduction to B?ttcher-Wenzel conjecture
8.2 The proof of B?ttcher-Wenzel conjecture
8.3 Maximal pairs of the inequality
8.4 Other related problems
8.4.1 The use of other norms in the inequality
8.4.2 The sharpening of the inequality
8.4.3 The extension to other products similar to the commutator
Bibliography
Index
应用矩阵分析导论 (英文版) [An Introduction to Applied Matrix Analys] 电子书 下载 mobi epub pdf txt
应用矩阵分析导论 (英文版) [An Introduction to Applied Matrix Analys]-so88
应用矩阵分析导论 (英文版) [An Introduction to Applied Matrix Analys] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
金小庆,黄锡荣 著
出版社: 高等教育出版社 ISBN:9787040449945 版次:1 商品编码:11909197 包装:精装 丛书名: 现代应用数学丛书 外文名称:An Introduction to Applied Matrix Analys 开本:16开 出版时间:2016-04-01 用纸:胶版纸 页数:130
内容简介
科学和工程中的大部分问题将纳入矩阵问题。本书提供了应用矩阵理论基础介绍,也包括近几年的一些新的结论。 本书包括8章,它包括扰动和误差分析; 求解线性系统的共轭梯度法和预处理技术;基于正交变换的小二乘法等。 后二章包括了该领域的一些全新进展。在第7章,我们构造矩阵函数优的预处理器。更确切地说,令 f 为一个矩阵函数。 给定一个矩阵A,有两种选择构造f(A) 预处理器。我们研究了不同矩阵函数的预处理器的性质。在第8章,我们研究Bottcher-Wenzel猜想并讨论相关问题。 本书可作为科学和工程系高年级本科生或者低年级研究生的教材。本书要求基础知识为各个学科都开设的基本的线性代数、微积分、数值分析和计算知识。 本书也可作为对应用矩阵理论感兴趣的计算科学研究人员参考。作者简介
金小庆,博士,为澳门大学数学系教授,他的研究领域为数值线性代数和科学计算。 他出版了7本著作并发表了90余篇学术论文,是很多国际期刊的编委。黄锡荣,博士,为澳门大学数学系副教授,他的研究领域为偏微分方程解析和数值解。
目录
Preface vii1. Introduction and Review
1.1 Basic symbols
1.2 Quadratic forms and positive definite matrices
1.2.1 Quadratic forms
1.2.2 Problems involving quadratic forms
1.2.3 Positive definite matrix
1.2.4 Other methods to determine the positive definiteness
1.3 Theorems for eigenvalues of symmetric matrices
1.4 Complex inner product spaces
1.5 Hermitian, unitary, and normal matrices
1.6 Kronecker product and Kronecker sum
2. Norms and Perturbation Analysis
2.1 Vector norms
2.2 Matrix norms
2.3 Perturbation analysis for linear systems
2.4 Error on floating point numbers
3. Least Squares Problems
3.1 Solution of LS problems
3.2 Perturbation analysis for LS problems
3.3 Orthogonal transformations
3.3.1 Householder reflections
3.3.2 Givens rotations
3.4 An algorithm based on QR factorization
3.4.1 QR factorization
3.4.2 A practical algorithm for LS problems
4. Generalized Inverses
4.1 Moore-Penrose generalized inverse
4.2 Basic properties
4.3 Relation to LS problems
4.4 Other generalized inverses
5. Conjugate Gradient Method
5.1 Steepest descent method
5.1.1 Steepest descent method
5.1.2 Convergence rate
5.2 Conjugate gradientmethod
5.2.1 Conjugate gradient method
5.2.2 Basic properties
5.2.3 Practical CG method
5.3 Preconditioning technique
6. Optimal and Superoptimal Preconditioners
6.1 Introduction to optimal preconditioner
6.1.1 Circulantmatrix
6.1.2 Optimal preconditioner
6.2 Linear operator c_U
6.2.1 Algebraic properties
6.2.2 Geometric properties
6.3 Stability
6.4 Superoptimal preconditioner
6.5 Spectral relation of preconditioned matrices
7. Optimal Preconditioners for Functions of Matrices
7.1 Optimal preconditioners for matrix exponential
7.2 Optimal preconditioners for matrix cosine and matrix sine
7.3 Optimal preconditioners for matrix logarithm
8. B?ttcher-Wenzel Conjecture and Related Problems
8.1 Introduction to B?ttcher-Wenzel conjecture
8.2 The proof of B?ttcher-Wenzel conjecture
8.3 Maximal pairs of the inequality
8.4 Other related problems
8.4.1 The use of other norms in the inequality
8.4.2 The sharpening of the inequality
8.4.3 The extension to other products similar to the commutator
Bibliography
Index
应用矩阵分析导论 (英文版) [An Introduction to Applied Matrix Analys] 电子书 下载 mobi epub pdf txt
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