当前位置: X-MOL 学术Numer. Algor. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On restarted and deflated block FOM and GMRES methods for sequences of shifted linear systems
Numerical Algorithms ( IF 2.1 ) Pub Date : 2020-09-09 , DOI: 10.1007/s11075-020-01007-3
Lakhdar Elbouyahyaoui , Mohammed Heyouni , Azita Tajaddini , Farid Saberi-Movahed

The problem of shifted linear systems is an important and challenging issue in a number of research applications. Krylov subspace methods are effective techniques for different kinds of this problem due to their advantages in large and sparse matrix problems. In this paper, two new block projection methods based on respectively block FOM and block GMRES are introduced for solving sequences of shifted linear systems. We first express the original problem explicitly by a sequence of Sylvester matrix equations whose coefficient matrices are obtained from the shifted linear systems. Then, we show the restarted shifted block FOM (rsh-BFOM) method and derive some of its properties. We also present a framework for the restarted shifted block GMRES (rsh-BGMRES) method. In this regard, we describe two variants of rsh-BGMRES, including (1) rsh-BGMRES with an unshifted base system that applies a fixed unshifted base system and (2) rsh-BGMRES with a variable shifted base system in which the base block system can change after restart. Furthermore, we consider the use of deflation techniques for improving the performance of the rsh-BFOM and rsh-BGMRES methods. Finally, some numerical experiments are conducted to demonstrate the effectiveness of the proposed methods.



中文翻译:

关于线性方程组序列的重新启动和放气的块FOM和GMRES方法

在许多研究应用中,线性系统移位的问题是一个重要且具有挑战性的问题。由于Krylov子空间方法在大型和稀疏矩阵问题中具有优势,因此是解决此类问题的有效技术。本文介绍了分别基于块FOM和块GMRES的两种新的块投影方法来求解线性位移系统的序列。我们首先通过一系列Sylvester矩阵方程式明确表达原始问题,该方程式的系数矩阵是从线性位移系统获得的。然后,我们显示重新启动的移位块FOM(rsh-BFOM)方法并推导其某些属性。我们还为重新启动的移位块GMRES(rsh-BGMRES)方法提供了一个框架。在这方面,我们描述了rsh-BGMRES的两个变体,包括(1)具有应用固定的未移位基础系统的未移位基础系统的rsh-BGMRES和(2)具有可变移位基础系统的rsh-BGMRES,其中基础块系统可以在重新启动后进行更改。此外,我们考虑使用放气技术来改善rsh-BFOM和rsh-BGMRES方法的性能。最后,进行了一些数值实验,以证明所提方法的有效性。

更新日期:2020-09-10
down
wechat
bug