A novel class of block methods based on the block AA T-Lanczos bi-orthogonalization process for matrix equations

Abstract

In this paper, we introduce a block AA T-Lanczos bi-orthogonalization process. Based on this new process, the block bi-conjugate residual (Bl-BCR) method is derived, which is also a generalization of bi-conjugate residual method. In order to accelerate the rate of convergence, we generate a stabilized and more smoothly converging variant of Bl-BCR using formal matrix-valued orthogonal polynomials. Finally, numerical experiments illustrate the effectiveness of these block methods.