GBi-CGSTAB(s, L): IDR(s) with higher-order stabilization polynomials

IDR(s) is now recognized as one of the most effective methods, often superior to other Krylov subspace methods, for large nonsymmetric linear systems of equations. In this paper we propose an improvement upon IDR(s) by incorporating a higher-order stabilization polynomial into IDR(s). The proposed algorithm, named GBi-CGSTAB(s, L), shares desirable features with both IDR(s) and Bi-CGSTAB(L).