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.
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页码：2514 / 2522
页数：9
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