Optimality Properties of Galerkin and Petrov-Galerkin Methods for Linear Matrix Equations

被引：11

作者：

Palitta, Davide ^{[1
]}

Simoncini, Valeria ^{[2
,3
]}

机构：

[1] Max Planck Inst Dynam Complex Tech Syst, Res Grp Computat Methods Syst & Control Theory CS, Sandtorstr 1, D-39106 Magdeburg, Germany

[2] Univ Bologna, Dipartimento Matemat, Alma Mater Studiorum, Piazza Porta San Donato 5, I-40127 Bologna, Italy

[3] CNR, IMATI, Pavia, Italy

来源：

VIETNAM JOURNAL OF MATHEMATICS | 2020年 / 48卷 / 04期

关键词：

Linear matrix equations; Large scale equations; Sylvester equation; KRYLOV-SUBSPACE METHODS; LOW-RANK METHODS; PROJECTION METHODS; SYMMETRIC SYLVESTER; LYAPUNOV EQUATIONS; ERROR ANALYSIS; CONVERGENCE; SYSTEMS; ALGORITHM;

D O I：

10.1007/s10013-020-00390-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Galerkin and Petrov-Galerkin methods are some of the most successful solution procedures in numerical analysis. Their popularity is mainly due to the optimality properties of their approximate solution. We show that these features carry over to the (Petrov-) Galerkin methods applied for the solution of linear matrix equations. Some novel considerations about the use of Galerkin and Petrov-Galerkin schemes in the numerical treatment of general linear matrix equations are expounded and the use of constrained minimization techniques in the Petrov-Galerkin framework is proposed.

引用

页码：791 / 807

页数：17

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