Block BiCGGR: a new Block Krylov subspace method for computing high accuracy solutions

Abstract

In this paper, the influence of errors which arise in matrix multiplications on the accuracy of approximate solutions generated by the Block BiCGSTAB method is analyzed. In order to generate high accuracy solutions, a new Block Krylov subspace method named “Block BiCGGR” is also proposed. Some numerical experiments illustrate that the Block BiCGGR method can generate high accuracy solutions compared with the Block BiCGSTAB method.