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BIT Numerical Mathematics

, Volume 47, Issue 1, pp 103–120 | Cite as

Iterative regularization with minimum-residual methods

  • T.K. Jensen
  • P.C. Hansen
Article

Abstract

We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES – their success as regularization methods is highly problem dependent.

Key words

iterative regularization discrete ill-posed problems GMRES RRGMRES MINRES MR-II Krylov subspaces 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.TNM ConsultHerlevDenmark
  2. 2.Informatics and Mathematical ModellingTechnical University of DenmarkLyngbyDenmark

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