Inheritance of the discrete Picard condition in Krylov subspace methods
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.
KeywordsDiscrete Picard condition Iterative regularization Arnoldi algorithm GMRES residual Lanczos bidiagonalization algorithm
Mathematics Subject Classification65F10 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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