Varieties of Product-type Method for Solving Large Non-Hermitian Linear Systems

Abstract For solving non-Hermitian linear systems, a famous method is Bi-Conjugate Gradient method (Bi-CG), but its performance is not usually satisfactory because of the unstable convergent behavior and the expensive computational cost. Recently a family of methods named Product-type methods were developed to enhance the Bi-CG method by redefining the residual vector as rn: = Hn(A)r B n, where