On Krylov solutions to infinite-dimensional inverse linear problems

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 a given inverse problem, together with a series of model examples and numerical e...

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Bibliographic Details
Published in:	Calcolo Vol. 56; no. 3; pp. 1 - 25
Main Authors:	Caruso, Noe, Michelangeli, Alessandro, Novati, Paolo
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.09.2019 Springer Nature B.V
Subjects:	Hilbert space Inverse problems Mathematics Mathematics and Statistics Numerical Analysis Theory of Computation Inverse linear problems Ill-posed problems Krylov subspaces CG Bounded linear operators LSQR Cyclic operators Self-adjoint operators Orthonormal basis discretisation 47N40 Krylov solution Infinite-dimensional Hilbert space 47A05 47B15 GMRES 47B34 65J10 65J22
ISSN:	0008-0624, 1126-5434
Online Access:	Get full text
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