On Krylov solutions to infinite-dimensional inverse linear problems
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Date
2018-11
Journal Title
Journal ISSN
Volume Title
Publisher
SISSA
Abstract
We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of the considered inverse problem. The presentation is based on theoretical results together with a series of model examples, and it is corroborated by specific numerical experiments.
Description
Keywords
inverse linear problems,, in nite-dimensional Hilbert space, ill-posed problems, orthonormal basis discretisation, bounded linear operators, Krylov subspaces, cyclic operators, Krylov solution, GMRES, conjugate gradient, LSQR.