Accuracy Improvement of the Block Product-type Iterative Methods for Linear Systems with Multiple Right-Hand Sides

Abstract

Abstract. The Block product-type iterative methods are efficient methods for solving linear systems with multiple right-hand sides. These methods can solve them simultaneously. However, when the number of right-hand sides is large, the accuracy of the approximate solution generated by these methods may deteriorate. One of the causes is a gap between the recursive residual matrix and the true residual matrix. In this paper, the Block GPBiCG method and the Block BiCGSTAB method are reconstructed for improving the accuracy of the approximate solutions. Moreover, we verify that the proposed methods are often better in accuracy through numerical experiments.