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Flexible and multi‐shift induced dimension reduction algorithms for solving large sparse linear systems |
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| Authors: | Martin B van Gijzen Gerard L G Sleijpen Jens‐Peter M Zemke |
| Institution: | 1. Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;2. Mathematical Institute, Utrecht University, 3508 TA Utrecht, The Netherlands;3. Institut für Mathematik, Technische Universit?t Hamburg‐Harburg, D‐21073 Hamburg, Germany |
| Abstract: | We give two generalizations of the induced dimension reduction (IDR) approach for the solution of linear systems. We derive a flexible and a multi‐shift quasi‐minimal residual IDR variant. These variants are based on a generalized Hessenberg decomposition. We present a new, more stable way to compute basis vectors in IDR. Numerical examples are presented to show the effectiveness of these new IDR variants and the new basis compared with existing ones and to other Krylov subspace methods. Copyright © 2014 John Wiley & Sons, Ltd. |
| Keywords: | iterative methods IDR IDR(s) quasi‐minimal residual Krylov subspace methods large sparse nonsymmetric linear systems |