A class of product-type Krylov-subspace methods for solving nonsymmetric linear systems

In the present paper, a class of product-type Krylov-subspace methods for solving nonsymmetric linear systems is discussed. A characteristic of this class is the relationship rn=Hn(A)rnBCG where rn is the residual vector corresponding to the nth iterate xn, and rnBCG is the nth residual generated in bi-conjugate gradient method. The polynomial Hn is chosen to speed up and stabilize convergence, while satisfying standard three-term recurrence relations. These product-type methods can be regarded as unifications and generalizations of CGS and Bi-CGSTAB.