Numerical Algorithms

, Volume 40, Issue 2, pp 201–216 | Cite as

Analysis of the convergence of the minimal and the orthogonal residual methods

Article

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.

Keywords

GMRES Krylov subspace methods convergence analysis 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques AppliquéesCentre Universitaire de la Mi-voixCalais CedexFrance

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