数值线性代数及其应用 本书特色

Numerical linear algebra， also called matrix computation， has beea cen-ter of scientific and engineering computing since 1946， the first modercom-puter was born. Most of problems iscience and engineering finally becomeproblems imatrix computation. Therefore， it is important for us to study nu-merical linear algebra. This book gives aelementary introductioto matrixcomputatioand it also includes some new results obtained irecent years.

数值线性代数及其应用 内容简介

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数值线性代数及其应用 目录

Preface
Chapter 1 Introduction
1．1 Basic symbols
1．2 Basic problems iNLA
1．3 Why shall we study numerical methods?
1．4 Matrix factorizations (decompositions)
1．5 Perturbatioand error analysis
1．6 Operatiocost and convergence rate
Exercises

Chapter 2 Direct Methods for Linear Systems
2．1 Triangular linear systems and LU factorization
2．2 LU factorizatiowith pivoting
2．3 Cholesky factorization
Exercises

Chapter 3 Perturbatioand Error Analysis
3．1 Vector and matrix norms
3．2 Perturbatioanalysis for linear systems
3．3 Error analysis ofloating point arithmetic
3．4 Error analysis opartial 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
7．5 Real versioof QR algorithm
Exercises

Chapter 8 Symmetric Eigenvalue Problems
8．1 Basic spectral properties
8．2 Symmetric QR method
8．3 Jacobi method
8．4 Bisectiomethod
8．5 Divide-and-conquer method
Exercises

Chapter 9 Applications
Bibliography
Index

自然科学 数学 代数数论组合理论

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