Abstract
Recently P. Sonneveld and M. van Gijzen proposed new IDR theorem extended from the original theorem. Their technical report, however, has imperfection of the IDR theorem and lack of description on implementation. In this paper, we consider two types of preconditioing of IDR(s) method. One of preconditionings is refered to as an easy preconditioning, and the other is refered to as a profound preconditioning. We consider on reliability of two types of preconditioning in view of accuracy of the approximate solutions and computational cost. In particular, we make clear that the amount of computational cost of right preconditioning is the least amount compared with left and two-sided preconditionings. Through two kinds of numerical experiments, we verify that profound right-preconditioning of IDR(s) method outperforms among other iterative methods from the viewpoint of CPU times and amount of memory.
