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內容簡介

　　Iterative Methods for Sparse Linear Systems， Second Edition gives an in-depth， up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative， i.e.， they provide sequences of approximations that will converge to the solution. This new edition includes a wide range of the best methods available today. The author has added a new chapter on multigrid techniques and has updated material throughout the text， particularly the chapters on sparse matrices， Krylov subspace methods， preconditioning techniques， and parallel preconditioners. Material on older topics has been removed or shortened， numerous exercises have been added， and many typographical errors have been corrected. The updated and expanded bibliography now includes more recent works emphasizing new and important research topics in this field. This book can be used to teach graduate-level courses on iterative methods for linear systems. Engineers and mathematicians will find its contents easily accessible， and practitioners and educators will value it as a helpful resource. The preface includes syllabi that can be used for either a semester- or quarter-length course in both mathematics and computer science.

內頁插圖

目錄

Preface to the Second Edition
Preface to the First Edition
1 Background in Linear Algebra
1．1 Matrices
1．2 Square Matrices and Eigenvalues
1．3 Types of Matrices
1．4 Vector Inner Products and Norms
1．5 Matrix Norms
1．6 Subspaces， Range， and Kernel
1．7 Orthogonal Vectors and Subspaces
1．8 Canonical Forms of Matrices
1．8．1 Reduction to the Diagonal Form
1．8．2 The Jordan Canonical Form
1．8．3 The Schur Canonical Form
1．8．4 Application to Powers of Matrices
1．9 Normal and Hermitian Matrices
1．9．1 Normal Matrices
1．9．2 Hermitian Matrices
1．10 Nonnegative Matrices， M-Matrices
1．11 Positive Definite Matrices
1．12 Projection Operators
1．12．1 Range and Null Space of a Projector
1．12．2 Matrix Representations
1．12．3 Orthogonal and Oblique Projectors
1．12．4 Properties of Orthogonal Projectors
1．13 Basic Concepts in Linear Systems
1．13．1 Existence of a Solution
1．13．2 Perturbation Analysis
Exercises
Notes and References

2 Discretization of Partial Differential Equations
2．1 Partial Differential Equations
2．1．1 Elliptic Operators
2．1．2 The Convection Diffusion Equation
2．2 Finite Difference Methods
2．2．1 Basic Approximations
2．2．2 Difference Schemes for the Laplacian Operator
2．2．3 Finite Differences for One-Dimensional Problerr
2．2．4 Upwind Schemes
2．2．5 Finite Differences for Two-Dimensional Problerr
2．2．6 Fast Poisson Solvers
2．3 The Finite Element Method
2．4 Mesh Generation and Refinement
2．5 Finite Volume Method
Exercises
Notes and References

3 Sparse Matrices
3．1 Introduction
3．2 Graph Representations
3．2．1 Graphs and Adjacency Graphs
3．2．2 Graphs of PDE Matrices
3．3 Permutations and Reorderings
3．3．1 Basic Concepts
3．3．2 Relations with the Adjacency Graph
3．3．3 Common Reorderings
3．3．4 Irreducibility
3．4 Storage Schemes
3．5 Basic Sparse Matrix Operations
3．6 Sparse Direct Solution Methods
3．6．1 MD Ordering
3．6．2 ND Ordering
3．7 Test Problems
Exercises
Notes and References

4 Basic Iterative Methods
4．1 Jacobi， Gauss-Seidel， and Successive Overrelaxation
4．1．1 Block Relaxation Schemes
4．1．2 Iteration Matrices and Preconditioning
4．2 Convergence
4．2．1 General Convergence Result
4．2．2 Regular Splittings
4．2．3 Diagonally Dominant Matrices
4．2．4 Symmetric Positive Definite Matrices
4．2．5 Property A and Consistent Orderings
……
5 Projection Methods
6 Krylov Subspace Methods， Part Ⅰ
7 Krylov Subspace Methods， Part Ⅱ
8 Methods Related to the Normal Equations
9 Preconditioned Iterations
10 Preconditioning Techniques
11 Parallel Implementations
12 Parallel Preconditioners
13 Multigrid Methods
14 Domain Decomposition Methods
Bibliography
Index

前言/序言

　　要使我國的數學事業更好地發展起來，需要數學傢淡泊名利並付齣更艱苦地努力。另一方麵，我們也要從客觀上為數學傢創造更有利的發展數學事業的外部環境，這主要是加強對數學事業的支持與投資力度，使數學傢有較好的工作與生活條件，其中也包括改善與加強數學的齣版工作。
　　從齣版方麵來講，除瞭較好較快地齣版我們自己的成果外，引進國外的先進齣版物無疑也是十分重要與必不可少的。科學齣版社影印一批他們齣版的好的新書，使我國廣大數學傢能以較低的價格購買，特彆是在邊遠地區工作的數學傢能普遍見到這些書，無疑是對推動我國數學的科研與教學十分有益的事。
　　這次科學齣版社購買瞭版權，一次影印瞭23本施普林格齣版社齣版的數學書，就是一件好事，也是值得繼續做下去的事情。大體上分一下，這23本書中，包括基礎數學書5本，應用數學書6本與計算數學書12本，其中有些書也具有交叉性質。這些書都是很新的，2000年以後齣版的占絕大部分，共計16本，其餘的也是1990年以後齣版的。這些書可以使讀者較快地瞭解數學某方麵的前沿，例如基礎數學中的數論、代數與拓撲三本，都是由該領域大數學傢編著的“數學百科全書”的分冊。對從事這方麵研究的數學傢瞭解該領域的前沿與全貌很有幫助。按照學科的特點，基礎數學類的書以“經典”為主，應用和計算數學類的書以“前沿”為主。這些書的作者多數是國際知名的大數學傢，例如《拓撲學》一書的作者諾維科夫是俄羅斯科學院的院士，曾獲“菲爾茲奬”和“沃爾夫數學奬”。這些大數學傢的著作無疑將會對我國的科研人員起到非常好的指導作用。
　　當然，23本書隻能涵蓋數學的一部分，所以，這項工作還應該繼續做下去。更進一步，有些讀者麵較廣的好書還應該翻譯成中文齣版，使之有更大的讀者群。總之，我對科學齣版社影印施普林格齣版社的部分數學著作這一舉措錶示熱烈的支持，並盼望這一工作取得更大的成績。
國外數學名著係列（續一 影印版）39：稀疏綫性係統的迭代方法（第二版） [Iterative Methods for Sparse Linear Systems(Secong Edition)] 下載 mobi epub pdf txt 電子書

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