简介
科学和工程中的大部分问题最终将纳入矩阵问题。《应用矩阵分析导论（英文版）》提供了应用矩阵理论基础介绍，也包括最近几年的一些新的结论。《应用矩阵分析导论（英文版）》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；基于正交变换的最小二乘法等。最后的二章包括了该领域的一些最新进展。在第7章，我们构造矩阵函数最优的预处理器。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) 最佳预处理器。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。《应用矩阵分析导论（英文版）》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。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。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。
目录
Preface vii
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.
...... 全部内容请购买实物书籍
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.
...... 全部内容请购买实物书籍
应用矩阵分析导论
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