Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems

被引：6
|
作者：
Axelsson, O. [1 ,2 ]
Karatson, J. [3 ,4 ,5 ]
机构：
[1] Inst Geon AS CR, Dept Appl Math & Comp Sci, Ostrava, Czech Republic
[2] Inst Geon AS CR, Dept IT4Innovat, Ostrava, Czech Republic
[3] ELTE Univ, Dept Appl Anal, Budapest, Hungary
[4] ELTE Univ, MTA ELTE Numer Anal & Large Networks Res Grp, Budapest, Hungary
[5] Tech Univ, Dept Anal, Budapest, Hungary
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2018年 / 39卷 / 09期
基金：
匈牙利科学研究基金会;
关键词：
Optimal control; preconditioners; superlinear convergence; EQUIVALENT OPERATORS; EQUATIONS; SOLVER;
D O I：
10.1080/01630563.2018.1431928
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Optimal control problems for PDEs arise in many important applications. A main step in the solution process is the solution of the arising linear system, where the crucial point is usually finding a proper preconditioner. We propose both proper block diagonal and more involved preconditioners, and derive mesh independent superlinear convergence of the preconditioned GMRES iterations based on a compact perturbation property of the underlying operators.
引用
收藏
页码：921 / 936
页数：16
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