AN ERROR ANALYSIS FOR RATIONAL GALERKIN PROJECTION APPLIED TO THE SYLVESTER EQUATION

被引：35

作者：

Beckermann, Bernhard ^{[1
]}

机构：

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

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 06期

关键词：

Sylvester equation; Lyapunov equation; Galerkin projection; rational Krylov spaces; ADI; NUMERICAL-SOLUTION; KRYLOV SUBSPACES; MODEL-REDUCTION; CONVERGENCE; RANGE;

D O I：

10.1137/110824590

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we suggest a new formula for the residual of Galerkin projection onto rational Krylov spaces applied to a Sylvester equation, and establish a relation to three different underlying extremal problems for rational functions. These extremal problems enable us to compare the size of the residual for the above method with that obtained by ADI. In addition, we deduce several new a priori error estimates for Galerkin projection onto rational Krylov spaces, both for the Sylvester and for the Lyapunov equation.

引用

页码：2430 / 2450

页数：21

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