BIT Numerical Mathematics

, Volume 56, Issue 3, pp 893–918 | Cite as

Inheritance of the discrete Picard condition in Krylov subspace methods

  • Silvia Gazzola
  • Paolo Novati


When projection methods are employed to regularize linear discrete ill-posed problems, one implicitly assumes that the discrete Picard condition (DPC) is somehow inherited by the projected problems. In this paper we show that, under some assumptions, the DPC holds for the projected uncorrupted systems computed by various Krylov subspace methods. By exploiting the inheritance of the DPC, some estimates on the behavior of the projected problems are also derived. Numerical examples are provided in order to illustrate the accuracy of the derived estimates.


Discrete Picard condition Iterative regularization  Arnoldi algorithm GMRES residual Lanczos bidiagonalization algorithm 

Mathematics Subject Classification

65F10 65F22 65R32 



We are grateful to the anonymous Referee and to the Editor for providing insightful suggestions that helped to expand and improve the paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di PadovaPadovaItaly
  2. 2.Dipartimento di Matematica e GeoscienzeUniversità di TriesteTriesteItaly

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