Print Email Facebook Twitter Exploiting BiCGstab(?) strategies to induce dimension reduction Title Exploiting BiCGstab(?) strategies to induce dimension reduction Author Sleijpen, G.L.G. Van Gijzen, M.B. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2010-08-31 Abstract IDR(s) [P. Sonneveld and M. B. van Gijzen, SIAM J. Sci. Comput., 31 (2008), pp. 1035–1062] and BiCGstab(?) [G. L. G. Sleijpen and D. R. Fokkema, Electron. Trans. Numer. Anal., 1 (1993), pp. 11–32] 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 describe IDRstab, a new method that combines the strengths of IDR(s) and BiCGstab(?). To derive IDRstab we extend the results that we reported on in [G. L. G. Sleijpen, P. Sonneveld, and M. B. van Gijzen, Appl. Numer. Math., (2009), DOI: 10.1016/j.apnum.2009.07.001], where we considered Bi-CGSTAB as an induced dimension reduction (IDR) method. We will analyze the relation between hybrid Bi-CG methods and IDR and introduce the new concept of the Sonneveld subspace as a common framework. Through numerical experiments we will show that IDRstab can outperform both IDR(s) and BiCGstab(?). Subject Bi-CGSTABBi-CGiterative linear solversKrylov subspace methodsinduced dimension reduction To reference this document use: http://resolver.tudelft.nl/uuid:5c2e5192-dfd0-4eec-bd3d-ced713274b0c DOI https://doi.org/10.1137/090752341 Publisher Society for Industrial and Applied Mathematics ISSN 1064-8275 Source SIAM Journal on Scientific Computing, 32 (5), 2010 Part of collection Institutional Repository Document type journal article Rights (c) 2010 The Author(s)Society for Industrial and Applied Mathematics Files PDF vanGijzen2010.pdf 1.32 MB Close viewer /islandora/object/uuid:5c2e5192-dfd0-4eec-bd3d-ced713274b0c/datastream/OBJ/view