On Reforming of Residual used in IDR(s)Stab(L) and GBi-CGSTAB(s, L) methods

Abstract

  The auto corrected technique for residual of IDR(s) method has been proposed. We would like to extend this technique to some advanced IDR(s) methods, that is, IDR(s)Stab(L) and GBi-CGSTAB(s, L) methods combined IDR(s) and BiCGSTAB(L) methods. Therefore, we devised Reforming of Residual using range of a coefficient vector as its extension. Through several numerical experiments, we will make clear effectiveness of the proposed Reforming of Residual.