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.

19 pages,14 figures, Submitted to CPC on Jan 7, 2012

References in corpus (5)

• Linear Algebraic Calculation of Green's function for Large-Scale Electronic Structure Theory
• Application of block Krylov subspace algorithms to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD
• An iterative method to compute the overlap Dirac operator at nonzero chemical potential
• Domain-wall and overlap fermions at nonzero quark chemical potential
• A nested Krylov subspace method to compute the sign function of large complex matrices