Krylov solvability under perturbations of abstract inverse linear problems

• Autorzy: Caruso Noè Angelo , Michelangeli Alessandro

Identyfikatory

DOI

10.1515/jaa-2022-2004

• Języki publikacji: EN

Abstrakty

EN

When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is said to be a Krylov solution. Krylov solvability of the inverse problem allows for solution approximations that, in applications, correspond to the very efficient and popular Krylov subspace methods. We study the possible behaviors of persistence, gain, or loss of Krylov solvability under suitable small perturbations of the infinite-dimensional inverse problem - the underlying motivations being the stability or instability of infinite-dimensional Krylov methods under small noise or uncertainties, as well as the possibility to decide a priori whether an infinite-dimensional inverse problem is Krylov solvable by investigating a potentially easier, perturbed problem.

Słowa kluczowe

EN

inverse linear problems; Krylov solvability; infinite-dimensional Hilbert space; Hausdorff distance; subspace perturbations; weak topology

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 1
• Strony: 3--29
• Opis fizyczny: Bibliogr. 43 poz.

Twórcy

autor

Caruso Noè Angelo

• Mathematical Institute in Opava, Silesian University in Opava, Na Rybníčku 626/1, CZ-746 01 Opava, Czech Republic

• https://orcid.org/0000-0002-2835-1895

autor

Michelangeli Alessandro

• Institute for Applied Mathematics and Hausdorff Center for Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).