Bounds for the entries of matrix functions with applications to preconditioning

被引:95
作者
Benzi, M
Golub, GH
机构
[1] Univ Calif Los Alamos Natl Lab, Sci Comp Grp, Los Alamos, NM 87545 USA
[2] Stanford Univ, Dept Comp Sci, Stanford, CA 94305 USA
来源
BIT | 1999年 / 39卷 / 03期
基金
美国国家科学基金会;
关键词
matrix functions; quadrature rules; Lanczos process; band matrices; exponential decay; preconditioned conjugate gradients;
D O I
10.1023/A:1022362401426
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
Let A be a symmetric matrix and let f be a smooth function defined on an interval containing the spectrum of A. Generalizing a well-known result of Demko, Moss and Smith on the decay of the inverse we show that when A is banded, the entries of f(A) are bounded in an exponentially decaying manner away from the main diagonal. Bounds obtained by representing the entries of f(A) in terms of Riemann-Stieltjes integrals and by approximating such integrals by Gaussian quadrature rules are also considered. Applications of these bounds to preconditioning are suggested and illustrated by a few numerical examples.
引用
收藏
页码:417 / 438
页数:22
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