Matrices, moments and quadrature II; How to compute the norm of the error in iterative methods

被引：76

作者：

Golub, GH

Meurant, G

机构：

[1] STANFORD UNIV,DEPT COMP SCI,STANFORD,CA 94305

[2] CEA,F-94195 VILLENEUVE ST GEO,FRANCE

来源：

BIT | 1997年 / 37卷 / 03期

基金：

美国国家科学基金会;

关键词：

iterative methods; error computation; conjugate gradient;

D O I：

10.1007/BF02510247

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper, we study the numerical computation of the errors in linear systems when using iterative methods. This is done by using methods to obtain bounds or approximations of quadratic forms u(T) A(-1)u, where A is a symmetric positive definite matrix and u is a given vector. Numerical examples are given for the Gauss-Seidel algorithm. Moreover, we show that using a formula for the A-norm of the error from Dahlquist, Golub and Nash [1978] very good bounds of the error can be computed almost for free during the iterations of the conjugate gradient method leading to a reliable stopping criterion.

引用

页码：687 / 705

页数：19