BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems

In the present paper, we introduce a new extension of the conjugate residual (CR) method for solving non-Hermitian linear systems with the aim of developing an alternative basic solver to the established biconjugate gradient (BiCG), biconjugate residual (BiCR) and biconjugate AA-orthogonal residual (BiCOR) methods. The proposed Krylov subspace method, referred to as the BiCGCR2 method, is based on short-term vector recurrences and is mathematically equivalent to both BiCR and BiCOR. We demonstrate by extensive numerical experiments that the proposed iterative solver has often better convergence performance than BiCG, BiCR and BiCOR. Hence, it may be exploited for the development of new variants of non-optimal Krylov subspace methods.