An alternative implementation of the IDRstab method saving vector updates

Abstract

The IDRstab method is often more effective than both IDR($s$) and BiCGstab($\ell$) for solving large nonsymmetric linear systems. However the computational costs for vector updates are expensive on the original implementation of IDRstab. In this paper, we propose a variant of IDRstab to reduce the computational cost; vector updates are saved. Numerical experiments demonstrate the efficiency of our variant of IDRstab for sparse linear systems.