On Krylov solutions to infinite-dimensional inverse linear problems
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Date
2018-11
Authors
Caruso, Noe
Michelangeli, Alessandro
Novati, Paolo
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.