A flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systems
Hong-Xiu Zhong, Xian-Ming Gu
TL;DR
This paper introduces two adaptive iterative algorithms based on simpler GMRES with deflated restarting and flexible preconditioning, significantly improving efficiency in solving shifted linear systems.
Contribution
The paper proposes novel algorithms that leverage deflated restarting and flexible preconditioning to enhance the efficiency of solving shifted linear systems.
Findings
Reduced number of matrix-vector products
Lower CPU time compared to existing methods
Effective in numerical experiments
Abstract
In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting strategy and flexible preconditioning can significantly reduce the number of matrix-vector products and the elapsed CPU time. Numerical experiments are reported to illustrate the performance and effectiveness of the proposed algorithms.
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