稀疏矩阵的迭代方法是一个重要的研究方向，对大型计算问题有极其重要的作用。该书是国际上该领域最权威的著作，被多所大学选作教材使用，本书包括十四个章节的内容。
本书可以使读者较快地了解数学稀疏线性系统方面的前沿知识，对从事这方面研究的数学家了解该领域的前沿与全貌也很有帮助。

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 Problems
2.2.4 Upwind Schemes
2.2.5 Finite Differences for Two-Dimensional Problems
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
……
4 Basic Iterative Methods
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