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An Introduction to Applied Matrix Analysis



科学和工程中的大部分问题最终将纳入矩阵问题。本书提供了应用矩阵理论基础介绍，也包括最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

作者：
金小庆 黄锡荣
定价：
49.00 元
出版时间：
2016-04-15
ISBN：
978-7-04-044994-5
物料号：
44994-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
数学应用
重点项目：
暂无
版面字数：
180千字
开本：
16开
装帧形式：
精装
页数：
130
最新
印次时间：
2016年01月
  • 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
                                                                          • 6.2.2 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. Böttcher-Wenzel Conjecture and Related Problems
                                                                                      • 8.1 Introduction to Böttcher-Wenzel conjecture
                                                                                        • 8.2 The proof of Böttcher-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

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