DELFT UNIVERSITY OF TECHNOLOGY REPORT 09-02 Exploiting BiCGstab(l) strategies to induce dimension reduction

IDR(s) [9] and BiCGstab(l) [5] are two of the most efficient short recurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best depends on the specific problem class. In this paper we derive a new method, that we call IDRstab, that that combines the strengths of IDR(s) and BiCGstab(l). To derive IDRstab we extend the results that we reported on in [7] where we considered Bi-CGSTAB as an IDR method. We will analyse the structure of IDR in detail and introduce the new concept of the Sonneveld space. Through numerical experiments we will show that IDRstab can outperform both IDR(s) and BiCGstab(l).