A variant of IDRstab with reliable update strategies for solving sparse linear systems

Abstract

The IDRStab method is often more effective than the IDR(s) method and the BiCGstab(ℓ) method for solving large nonsymmetric linear systems. IDRStab can have a large so-called residual gap: the convergence of recursively computed residual norms does not coincide with that of explicitly computed residual norms because of the influence of rounding errors. We therefore propose an alternative recursion formula for updating the residuals to narrow the residual gap. The formula requires extra matrix–vector multiplications, but we reduce total computational costs by giving an alternative implementation which reduces the number of vector updates. Numerical experiments show that the alternative recursion formula reliably reduces the residual gap, and that our proposed variant of IDRStab is effective for sparse linear systems.