H-矩阵研究的新进展（英文版）

　　《H-矩阵类的理论及应用》专门研究具有广泛应用背景的H-矩阵类。全书共5章，第1章介绍有关的预备知识；第2章至第4章详细阐述正定矩阵类、稳定矩阵类、对角占优矩阵类、M-矩阵类和H-矩阵类等的定义、结构、性质、判定方法，以及几类矩阵之间的密切联系。第5章介绍几类矩阵在数值计算、齐次Markov过程、投入产出分析等方面的应用。 《H-矩阵类的理论及应用》取材丰富，反映了这些矩阵类研究的全新进展，可作为高等院校理工科研究生和数学专业高年级本科生的教学用书，也可作为相关专业科研和技术人员的参考用书。

暂缺《H-矩阵研究的新进展（英文版）》作者简介

Contents
Preface
PART ONE POINT H-MATRICES
Chapter 1 Introduction 3
1.1 Speaking from diagonally dominant matrices 4
1.2 H-matrices 6
1.3 The relationship between diagonally dominant matrices and H-matrices 8
Chapter 2 Nonsingularity/Singularity on H-matrices 10
2.1 Introduction 10
2.2 On critical conditions for nonsingularity of nonstrictly diagonally dominant matrices 11
2.3 Nonsingularity/singularity of nonstrictly diagonally dominant matrices 18
2.4 Further results on nonsingularity/singularity of nonstrictly diagonally dominant matrices 21
2.5 Nonsingularity/singularity of general H-matrices 24
2.6 Conclusion 27 Chapter 3 The Schur Complements of General H-matrices 28
3.1 Introduction 28
3.2 The Schur complement 28
3.3 Some classical results on the Schur complement of H-matrices 31
3.4 The Schur complements of strong H-matrices 33
3.5 The Schur complements of weak H-matrices 36
3.5.1 The Schur complements of degenerate H-matrices 37
3.5.2 The Schur complements of mixed H-matrices 39
3.5.3 Further results on the Schur complements of H-matrices 52
3.6 The generalized Schur complements of weak H-matrices 68
Chapter 4 The Eigenvalue Distribution on H-matrices and Their Schur Complements 72
4.1 Introduction 72
4.2 The eigenvalue distribution on nonstrictly diagonally dominant matrices and general H-matrices 73
4.3 The eigenvalue distribution on the Schur complements of H-matrices 76
4.4 The eigenvalue distribution on the generalized Schur complements of H-matrices 85
4.5 The generalized eigenvalue distribution on H-matrix pair 87
4.5.1 Some notions and preliminary results 87
4.5.2 The generalized eigenvalue distribution of diagonally dominant matrices pairs 88
4.5.3 The Generalized Eigenvalue Distribution of H-matrix pairs 92
4.5.4 The generalized eigenvalue location of some special matrix pairs 95
Chapter 5 Convergence on the Basic Iterative Methods for H-Matrices 97
5.1 Introduction 97
5.2 The Jacobi iterative method 97
5.3 The Gauss-Seidel iterative methods 101
5.3.1 Introduction 101
5.3.2 Some classic results 103
5.3.3 Convergence on Gauss-Seidel iterative methods 104
5.3.4 Convergence on symmetric Gauss-Seidel iterative method 109
5.3.5 Conclusions and remarks 112
5.3.6 Convergence on preconditioned Gauss-Seidel iterative methods 114
5.3.7 Numerical examples 117
5.3.8 Conclusions 120
5.4 The SOR iterative methods 120
5.4.1 Introduction 120
5.4.2 Some classic results 122
5.4.3 Convergence on FSOR and BSOR iterative methods 122
5.4.4 Convergence on SSOR iterative method 126
5.4.5 Numerical examples 130
5.4.6 Further work 133
5.5 The AOR iterative methods 133
5.5.1 Introduction 133
5.5.2 Convergence on FAOR and BAOR iterative methods 135
5.5.3 Convergence on SAOR iterative method 139
5.5.4 Numerical examples 143
5.5.5 Conclusion 149
Chapter 6 Radial Matrices and Asymptotical Stability of Linear Dynamic Systems 150
6.1 Introduction 150
6.2 Some notations and preliminary results 151
6.3 Some necessary and su.cient conditions on ∞-radial matrices (1-radial matrices) 154
6.4 Some properties on ∞-radial matrices (1-radial matrices) 156
6.5 Applications in the linear discrete dynamic systems 158
6.6 Conclusions 160
PART TWO GENERALIZATIONS OF H-MATRICES
Chapter 7 Two Generalizations of H-matrices 163
7.1 Introduction 163
7.2 Block Diagonally Dominant Matrices and Block H-matrices 165
7.3 Generalized H-matrices and extended H-matrices 169
Chapter 8 Block Diagonally Dominant Matrices and Block H-matrices 177
8.1 Nonsingularity/singularity on block diagonally dominant matrices and block H-matrices 177
8.2 The Schur complement of block diagonally dominant matrices and block H-matrices 179
8.2.1 The Schur complement of block diagonally dominant matrices 179
8.2.2 The Schur complement of block H-matrices 189
8.3 The eigenvalue distribution of block H-matrices 191
8.3.1 Some generalizations of Taussky’s theorem 192
8.3.2 The eigenvalue distribution of block diagonally dominant matrices and block H-matrices 198
Chapter 9 Generalized H-matrices 204
9.1 Nonsingularity/singularity on generalized H-matrices 204
9.2 Convergence of block iterative methods for linear systems with generalized H-matrices 204
9.2.1 Convergence of block iterative methods for generalized H-matrices 207
9.2.2 Some applications to special cases from the computations of partial di.erential equations 214
9.2.3 Numerical examples 217
9.2.4 Conclusion 220
9.3 On parallel multisplitting block iterative methods for linear systems with generalized H-matrices 220
9.3.1 On parallel multisplitting block iterative methods 221
9.3.2 Main results 223
9.3.3 Applications to special cases from the solution of partial di.erential equations 227
9.3.4 Numerical