Block conjugate gradient type methods for the approximation of bilinear form [formula omitted

Abstract

In this paper, we consider computing the approximation of block bilinear form CHA−1B, where square matrix A is large sparse, and B and C are rectangular matrices with the same size. We propose block conjugate gradient (CG) type methods for the approximation of CHA−1B, in which approximation Xk of linear systems AX=B does not need to be computed explicitly and only the approximation ηk of CHA−1B, which is mathematically equivalent to CHXk, will be calculated instead. Numerical results show the effectiveness of our proposed methods.