数值线性代数及其应用

Numerical linear algebra, also called matrix computation, has been a center of scientific and engineering computing since 1946. Most of problems in science and engineering finally become problems in matrix computations. This book gives an elementary introduction to matrix computation and it also includes some new results obtained in recent years. .
This book consists of nine chapters. It includes the Gaussian elimination, classical iterative methods and Krylov subspace methods for solving linear systems; the perturbation analysis of linear systems; the rounding error analysis of elimination; the orthogonal decompositions for solving linear least squares problem; and some classical methods for eigen-problems. In the last chapter, a brief survey of the latest developments in using boundary value methods for solving initial value problems of ordinary differential equations is given. ..
This is texbook for the senior students majoring in scientific computing and information science. It will be also useful to all who teach or study the subject. ...

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
3.1 Vector and matrix norms
3.2 Perturbation analysis for linear systems
3.3 Error analysis on floating point arithmetic

Numerical linear algebra, also called matrix computation, has been a center of scientific and engineering computing since 1946, the first modern com- puter was born. Most of problems in science and engineering finally become problems in matrix computation. Therefore, it is important for us to study numerical linear algebra. This book gives an elementary introduction to matrix computation and it also includes some new results obtained in recent years. In the beginning of this book, we first give an outline of numerical linear algebra in Chapt..