Print Email Facebook Twitter On the Convergence Behavior of IDR(s) and Related Methods Title On the Convergence Behavior of IDR(s) and Related Methods Author Sonneveld, P. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2012-09-25 Abstract An explanation is given of the convergence behavior of IDR(s) methods. The convergence mechanism of these algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behavior of Lanczos polynomials that occur in the theoretical description. This part of the residual polynomials is related to Lanczos methods with s left starting vectors, as described in a paper by Yeung and Chan on their ML(k)BiCGSTAB method, in [SIAM J. Sci. Comput., 21 (1999), pp. 1263--1290]. In this paper, the behavior of the second component is compared with the full GMRES method [SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856--869] and an expected rate of convergence is given, based on a random choice of the s shadow vectors Subject iterative methodsIDRKrylov subspace methodsBi-CGSTABnonsymmetric linear systems To reference this document use: http://resolver.tudelft.nl/uuid:13328fa2-8ebb-4846-aa44-a6cefbd94560 DOI https://doi.org/10.1137/100789889 Publisher Society for Industrial and Applied Mathematics (SIAM) ISSN 1064-8275 Source SIAM Journal on Scientific Computing, 34 (5), 2012 Part of collection Institutional Repository Document type journal article Rights © 2012 SIAM Files PDF Sonneveld_2012.pdf 704.28 KB Close viewer /islandora/object/uuid:13328fa2-8ebb-4846-aa44-a6cefbd94560/datastream/OBJ/view