A quasi-minimal residual variant of the BiCORSTAB method for nonsymmetric linear systems

Abstract

The Biconjugate A-orthogonal residual stabilized method named as BiCORSTAB was proposed by Jing et al. (2009), where the numerical experiments therein demonstrate that the BiCORSTAB method converges more smoothly than the Bi-Conjugate Gradient stabilized (BiCGSTAB) method in some circumstances. In order to further stabilize the convergence behavior and hopefully to accelerate the convergence speed of the BiCORSTAB algorithm when it has erratic convergence curves, a quasi-minimal residual variant of the BiCORSTAB algorithm, named as QMRCORSTAB, will be developed and investigated for solving nonsymmetric systems of linear equations borrowing the same further-smooth-effect idea for the QMRCGSTAB method. Numerical experiments on typical sets of both sparse and dense matrices will show that the proposed QMRCORSTAB method shares attractive smoother effect over its basic parent and also outperforms its counterpart.