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| 內容簡介： |
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袁锦昀教授是杰出的旅居巴西华人1957年出生于江苏兴化唐刘镇，1977年考入南京工学院，巴西巴拉那联邦大学数学系终身教授、工业数学研究所所长，巴西计算和应用数学学会副会长，巴西数学会巴拉那州分会会长，巴西科技部基金委数学终审组应用数学和计算数学负责人，巴西巴拉那基金委数学终身组成员。 《实用迭代分析（英文版）（精）》是由其创作的英文版实用迭代分析专著。
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Preface to the Series in Information and Computational Science
Preface
Chapter 1 Introduction
1.1 Background in linear algebra
1.1.1 Basic symbols, notations, and definitions
1.1.2 Vector norm
1.1.3 Matrix norm
1.1.4 Spectral radii
1.2 Spectral results of matrix
1.3 Special matrices
1.3.1 Reducible and irreducible matrices
1.3.2 Diagonally dominant matrices
1.3.3 Nonnegative matrices
1.3.4 p-cyclic matrices
1.3.5 Toeplitz, Hankel, Cauchy, Cauchy-like and Hessenberg matrices "
1.4 Matrix decomposition
1.4.1 LU decomposition
1.4.2 Singular value decomposition
1.4.3 Conjugate decomposition
1.4.4 QZ decomposition
1.4.5 S T decomposition
1.5 Exercises
Chapter 2 Basic Methods and Convergence
2.1 Basic concepts
2.2 The Jacobi method
2.3 The Gauss-Seidel method
2.4 The SOR method
2.5 M-matrices and splitting methods
2.5.1 M-matrix
2.5.2 Splitting methods
2.5.3 Comparison theorems
2.5.4 Multi-splitting methods
2.5.5 Generalized Ostrowski-Reich theorem
2.6 Error analysis of iterative methods
2.7 Iterative refinement
2.8 Exercises
Chapter 3 Non-stationary Methods
3.1 Conjugate gradient methods
3.1.1 Steepest descent method
3.1.2 Conjugate gradient method
3.1.3 Preconditioned conjugate gradient method
3.1.4 Generalized conjugate gradient method
3.1.5 Theoretical results on the conjugate gradient method
3.1.6 GeueuAzed poduct-tpe methods base u -QC
3.1.7 Inexact preconditioned conjugate gradient method
3.2 Lanczos method
3.3 GMRES method and QMR method
3.3.1 GMRES method
3.3.2 QMR method
3.3.3 Variants of the QMR method
3.4 Direct projection method
3.4.1 Theory of the direct projection method
3.4.2 Direct projection algorithms
3.5 Semi-conjugate direction method
3.5.1 Semi-conjugate vectors
3.5.2 Left conjugate direction method
3.5.3 One possible way to find left conjugate vector set
3.5.4 Remedy for breakdown
3.5.5 Relation with Gaussian elimination
3.6 Krylov subspace methods
3.7 Exercises
Chapter 4 Iterative Methods for Least Squares Problems
4.1 Introduction
4.2 Basic iterative methods
4.3 Block SOR methods
4.3.1 Block SOR algorithms
4.3.2 Convergence and optimal factors
4.3.3 Example
4.4 Preconditioned conjugate gradient methods
4.5 Generalized least squares problems
4.5.1 Block SOR methods
4.5.2 Preconditioned conjugate gradient method
4.5.3 Comparison
4.5.4 SOR-like methods
4.6 Rank deficient problems
4.6.1 Augmented system of normal equation
4.6.2 Block SOR algorithms
4.6.3 Convergence and optimal factor
4.6.4 Preconditioned conjugate gradient method
4.6.5 Comparison results
4.7 Exercises
Chapter 5 Preconditioners
5.1 LU decomposition and orthogonal transformations
5.1.1 Gilbert and Peierls algorithm for LU decomposition
5.1.2 Orthogonal transformations
5.2 Stationary preconditioners
5.2.1 Jacobi preconditioner
5.2.2 SSOR preconditioner
5.3 Incomplete factorization
5.3.1 Point incomplete factorization
5.3.2 Modified incomplete factorization
5.3.3 Block incomplete factorization
5.4 Diagonally dominant preconditioner
5.5 Preconditioner for least squares problems
5.5.1 Preconditioner by LU decomposition
5.5.2 Preconditioner by direct projection method
5.5.3 Preconditioner by QR decomposition
5.6 Exercises
Chapter 6 Singular Linear Systems
6.1 Introduction
6.2 Properties of singular systems
6.3 Splitting methods for singular systems
6.4 Nonstationary methods for Singular systems
6.4.1 symmetric and positive semidefinite systems
6.4.2 General systems
6.5 Exercises
Bibliography
Index
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