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