New Advances in Research on H-matrices-H-矩阵研究的新进展_PDF下载[71MB-百度云]张成毅

ContentsPrefacePART ONE POINT H-MATRICESChapter 1 Introduction 31.1 Speaking from diagonally dominant matrices 41.2 H-matrices 61.3 The relationship between diagonally dominant matrices and H-matrices 8 Chapter 2 Nonsingularity/Singularity on H-matrices 10 2.1 Introduction 102.2 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 242.6 Conclusion 27 Chapter 3 The Schur Complements of General H-matrices 28 3.1 Introduction 283.2 The Schur complement 283.3 Some classical results on the Schur complement of H-matrices 31 3.4 The Schur complements of strong H-matrices 333.5 The Schur complements of weak H-matrices 363.5.1 The Schur complements of degenerate H-matrices 373.5.2 The Schur complements of mixed H-matrices 39 3.5.3 Further results on the Schur complements of H-matrices 523.6 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 724.2 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 975.2 The Jacobi iterative method 975.3 The Gauss-Seidel iterative methods 1015.3.1 Introduction 1015.3.2 Some classic results 103 5.3.3 Convergence on Gauss-Seidel iterative methods 1045.3.4 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 1145.3.7 Numerical examples 1175.3.8 Conclusions 120 5.4 The SOR iterative methods 1205.4.1 Introduction 1205.4.2 Some classic results 122 5.4.3 Convergence on FSOR and BSOR iterative methods 122 5.4.4 Convergence on SSOR iterative method 1265.4.5 Numerical examples 1305.4.6 Further work 133 5.5 The AOR iterative methods 1335.5.1 Introduction 1335.5.2 Convergence on FAOR and BAOR iterative methods 1355.5.3 Convergence on SAOR iterative method 139 5.5.4 Numerical examples 1435.5.5 Conclusion 149 Chapter 6 Radial Matrices and Asymptotical Stability of Linear Dynamic Systems 150 6.1 Introduction 1506.2 Some notations and preliminary results 1516.3 Some necessary and su.cient conditions on ∞-radial matrices (1-radial matrices) 154 6.4 Some properties on ∞-radial matrices (1-radial matrices) 1566.5 Applications in the linear discrete dynamic systems 1586.6 Conclusions 160PART TWO GENERALIZATIONS OF H-MATRICES Chapter 7 Two Generalizations of H-matrices 1637.1 Introduction 1637.2 Block Diagonally Dominant Matrices and Block H-matrices 165 7.3 Generalized H-matrices and extended H-matrices 169Chapter 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 1918.3.1 Some generalizations of Taussky’s theorem 1928.3.2 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 2179.2.4 Conclusion 220 9.3 On parallel multisplitting block iterative methods for linear systems with generalized H-matrices 2209.3.1 On parallel multisplitting block iterative methods 221 9.3.2 Main results 2239.3.3 Applications to special cases from the solution of partial di.erential equations 2279.3.4 Numerical