Analysis of the convergence of the minimal and the orthogonal residual methods |
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Authors: | Email author" target="_blank">H?SadokEmail author |
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Institution: | (1) Laboratoire de Mathématiques Appliquées, Centre Universitaire de la Mi-voix, Batiment H. Poincaré, 50 rue F. Buisson, B.P. 699, F-62228 Calais Cedex, France |
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Abstract: | We consider two Krylov subspace methods for solving linear systems, which are the minimal residual method and the orthogonal
residual method. These two methods are studied without referring to any particular implementations. By using the Petrov–Galerkin
condition, we describe the residual norms of these two methods in terms of Krylov vectors, and the relationship between there
two norms. We define the Ritz singular values, and prove that the convergence of these two methods is governed by the convergence
of the Ritz singular values.
AMS subject classification 65F10 |
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Keywords: | GMRES Krylov subspace methods convergence analysis |
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