數值線性代數及其套用（英文）

圖書前言

Numerical linear algebra， also called matrix computation， has been a cen-ter of scientific and engineering computing since 1946， the first modern com-puter was born. Most of problems in science and engineering finally becomeproblems in matrix computation. Therefore， it is important for us to study nu-merical linear algebra. This book gives an elementary introduction to matrixcomputation and it also includes some new results obtained in recent years. Inthe beginning of this book， we first give an outline of numerical linear algebrain Chapter 1.

In Chapter 2， we introduce Gaussian elimination， a basic direct method，for solving general linear systems. Usually， Gaussian elimination is used forsolving a dense linear system with median size and no special structure. Theoperation cost of Gaussian elimination is O（n3） where n is the size of thesystem. The pivoting technique is also studied.

In Chapter 3， in order to discuss effects of perturbation and error on nu-merical solutions， we introduce vector and matrix norms and study their prop-erties. The error analysis on floating point operations and on partial pivotingtechnique is also given.

In Chapter 4， linear least squares problems are studied. We will concen-trate on the problem of finding the least squares solution of an overdeterminedlinear system Ax = b where A has more rows than columns. Some orthog-onal transformations and the QR decomposition are used to design efficientalgorithms for solving least squares problems.

數值線性代數及其套用（英文）

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圖書前言

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