A SQMRCGstab Algorithm for Families of Shifted Linear Systems
Abstract
This study is mainly focused on iterative solutions to shifted linear systems arising from a Quantum Chromodynamics (QCD) problem. To solve such system efficiently, we explore a kind of shifted QMRCGstab (SQMRCGstab) methods, which is derived by extending the quasi-minimum residual to the shifted BiCGstab. The shifted QMRCGstab method takes advantage of the shifted structure, so that the number of matrix-vector products and the number of inner products are the same as a single linear system. Moreover, the SQMRCGstab achieves a smoothing of the residual compared to the shifted BiCGstab, and is more competitive than the MS-QMRIDR(s) and the shifted BiCGstab on the QCD problem. Numerical examples show also the efficiency of the method when one applies it to the real problems.
Keywords
Cite
@article{arxiv.1305.5737,
title = {A SQMRCGstab Algorithm for Families of Shifted Linear Systems},
author = {Jing Meng and Pei-yong Zhu and Hou-Biao Li},
journal= {arXiv preprint arXiv:1305.5737},
year = {2013}
}
Comments
19 pages,14 figures, Submitted to CPC on Jan 7, 2012