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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Summary: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 experiments.
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content type line 14
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-019-0330-7