Robust preconditioners for optimal control with time-periodic parabolic equation

被引：2

作者：

Liao, Li-Dan ^{[1
,2
]}

Zhang, Guo-Feng ^{[1
]}

Zhang, Lei ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China

[2] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 76卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Preconditioner; Schur complement approximation; Optimal parameter; Time-periodic parabolic equation; Spectral properties; KRYLOV SUBSPACE METHODS; 2-BY-2; LINEAR-SYSTEMS; ITERATION METHODS;

D O I：

10.1016/j.camwa.2018.08.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on a new approximation of a Schur complement matrix and some preconditioning techniques considered in earlier papers, three robust preconditioners are presented for solving the KKT systems arising from discretizing optimal control problem with time-periodic parabolic equation. The eigenvalue bounds of the preconditioned matrices and some new theoretical results are obtained. Moreover, selection of quasi-optimal parameter is studied and an explicit expression of the quasi-optimal parameter is given. Numerical examples are given to illustrate the effectiveness of the three proposed optimized preconditioners. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：2514 / 2522

页数：9

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