数值线性代数及其应用
作者：金小庆著
出版时间：2004
内容简介
《数值线性代数及其应用》是为大学数学系信息与计算专业本科生编写的《数值代数》课英文版教材。《数值线性代数及其应用》共分九章，内容包括：引言；求解线性方程组的直接解法；扰动和误差分析；最小二乘问题；经典迭代法；Krylov子空间方法；非对称特征值问题；对称特征值问题和在求解常微分方程中的应用。《数值线性代数及其应用》用简练的英语介绍了该课程的基本知识，同时介绍了国际上流行的Krylov子空间迭代法和GMRES方法，还结合作者最新的科研成果，用Strang型预条件来求解延迟型常微分方程。《数值线性代数及其应用》可作为综合大学、理工科大学或高等师范学校的计算数学、应用数学和工程计算等专业的本科生教材或教学参考书，也可供从事科学与工程计算的科技人员参考。适合于国内正在推广的双语教学。
目录
Contents
Preface
Chapter 1 Introduction
1.1 Basic symbols
1.2 Basic problems in NLA
1.3 Why shall we study numerical methods?
1.4 Matrix factorizations (decompositions)
1.5 Perturbation and error analysis
1.6 Operation cost and convergence rate
Exercises

Chapter 2 Direct Methods for Linear Systems
2.1 Triangular linear systems and LU factorization
2.2 LU factorization with pivoting
2,3 Cholesky factorization
Exercises

Chapter 3 Perturbation and Error Analysis
31I Vector and matrix norms
3.2 Perturbation analysis for linear systems
3.3 Error analysis on floating point arithmetic
3.4 Error analysison partial pivoting
Exercises

Chapter 4 Least Squares Problems
4.1 Least squares problems
4.2 Orthogonal transformations
4.3 QR decomposition
Exercises

Chapter 5 Classical Iterative Methods
5.1 Jacobi and Gauss-Seidel method
5.2 Convergence analysis
5.3 Convergence rate
5.4 SOR method
Exercises

Chapter 6 Krylov Subspace Methods
6.1 Steepest descent method
6.2 Conjugate gradient method
6.3 Practical CG method and convergence analysis
6.4 Preconditioning
6.5 GMRES method
Exercises

Chapter 7 Nonsymmetric Eigenvalue Problems
7.1 Basic properties
7.2 Power method
7.3 Inverse power method
7.4 QR method
Exercises

Chapter 8 Symmetric Eigenvalue Problems
8.1 Basic spectral properties
8.2 Symmetric QR method
8.3 Jacobi method
8.4 Bisection method
8.5 Divide-and-conquer method
Exercises

Chapter 9 Applications
9.1 Introduction
9.2 Background of BVMs
9.3 Strang-type preconditioner for ODEs
9.4 Strang-type preconditioner for DDEs
9.5 Strang-type preconditioner for NDDEs
9.6 Strang-type preconditioner for SPDDEs
Bibliography
Index