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

被引：0
作者：
Davide Palitta
Valeria Simoncini
机构：
[1] Max Planck Institute for Dynamics of Complex Technical Systems,Research Group Computational Methods in Systems and Control Theory (CSC)
[2] Alma Mater Studiorum Università di Bologna,Dipartimento di Matematica
[3] IMATI-CNR,undefined
来源：
Vietnam Journal of Mathematics | 2020年 / 48卷
关键词：
Linear matrix equations; Large scale equations; Sylvester equation; 65F10; 65F30; 15A06;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：791 / 807
页数：16
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