AN ERROR ANALYSIS OF GALERKIN PROJECTION METHODS FOR LINEAR SYSTEMS WITH TENSOR PRODUCT STRUCTURE

被引：9

作者：

Beckermann, Bernhard ^{[1
]}

Kressner, Daniel ^{[2
]}

Tobler, Christine ^{[2
]}

机构：

[1] UST Lille, UFR Math M3, Lab Painleve UMR ANO EDP 8524, F-59655 Villeneuve Dascq, France

[2] EPF Lausanne, MATHICSE, ANCHP, CH-1015 Lausanne, Switzerland

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2013年 / 51卷 / 06期

关键词：

linear system; Kronecker product structure; Sylvester equation; tensor projection; Galerkin projection; rational Krylov subspaces; KRYLOV SUBSPACE METHODS; LYAPUNOV; APPROXIMATION; EQUATIONS;

D O I：

10.1137/120900204

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recent results on the convergence of a Galerkin projection method for the Sylvester equation are extended to more general linear systems with tensor product structure. In the Hermitian positive definite case, explicit convergence bounds are derived for Galerkin projection based on tensor products of rational Krylov subspaces. The results can be used to optimize the choice of shifts for these methods. Numerical experiments demonstrate that the convergence rates predicted by our bounds appear to be sharp.

引用

页码：3307 / 3326

页数：20

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