Development and performance evaluation of the Block-product type iterative methods with the variable grouping strategy

Abstract

The group-wise updating technique is one of the techniques for improving the accuracy of an approximate solution of Block Krylov subspace methods. This technique improves the accuracy of the approximate solution by grouping update terms of a recurrence relation. However, the number of update terms affects the performance of the Block Krylov subspace methods. This paper proposes a variable grouping strategy that does not fix the number of update terms to be grouped. Moreover, we incorporate the proposed strategy into the Block product-type iterative methods and evaluate its performance through numerical experiments.