An enhancement of the convergence of the IDR method

In this paper, we consider a family of algorithms, called IDR, based on the induced dimension reduction theorem. IDR is efficient short recurrence methods introduced by Sonneveld and Van Gijzen for solving large systems nonsymmetric linear equations. These generate residual vectors that live in sequence nested subspaces. We present IDR(s) method give two improvements its convergence. also define global version describe partial complete improvement Moreover, recall block state improvements. Numerical experiments are provided to illustrate performances derived algorithms compared well-known classical GMRES bi-conjugate gradient stabilized with single right-hand side, as well GMRES, stabilized, multiple sides.