An MHSS-like iteration method for two-by-two linear systems with application to FDE optimization problems

被引:3
作者
Zeng, Min-Li [1 ,2 ]
Zhang, Guo-Feng [3 ]
机构
[1] Putian Univ, Sch Math & Finance, Putian 351100, Peoples R China
[2] Fujian Normal Univ, Fujian Key Lab Math Anal & Applicat, Fuzhou 350117, Fujian, Peoples R China
[3] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
基金
中国国家自然科学基金;
关键词
MHSS iteration method; Circulant matrix; Two-by-two linear systems; Convergence; Discretized linear systems; FRACTIONAL CALCULUS; SPLITTING ITERATION; CIRCULANT; DIFFUSION; EQUATION; PRECONDITIONERS;
D O I
10.1016/j.cam.2018.11.030
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we exploit the numerical solvers for a fractional differential equations (FDE) optimization problem with constraints given by fractional elliptic state equations. The discretized linear system can be rewritten as a two-by-two linear system. By making use of the strategy of modified Hermitian and skew-Hermitian splitting (MHSS) iteration method proposed by Bai, we propose an MHSS-like iteration method. Comparing with the MHSS iteration method, the MHSS-like method only requires one to solve the two-by-two linear systems by a sparse Cholesky factorization and a fast Fourier transform. Hence, the MHSS-like method has less workload than the MHSS method. The convergence properties and the quasi-optimal parameters are analyzed in detail. Numerical examples are used to testify the efficiency of the new method. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码:368 / 381
页数:14
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