A note on preconditioning for indefinite linear systems

被引：427

作者：

Murphy, MF

Golub, GH

Wathen, AJ

机构：

[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

[2] Stanford Univ, Dept Comp Sci, Stanford, CA 94305 USA

[3] Univ Oxford, Comp Lab, Oxford OX1 3QD, England

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2000年 / 21卷 / 06期

关键词：

indefinite matrices; preconditioning;

D O I：

10.1137/S1064827599355153

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Preconditioners are often conceived as approximate inverses. For nonsingular indefinite matrices of saddle-point (or KKT) form, we show how preconditioners incorporating an exact Schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues. Thus approximations of the Schur complement lead to preconditioners which can be very effective even though they are in no sense approximate inverses.

引用

页码：1969 / 1972

页数：4

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