J
2023
Krylov solvability under perturbations of abstract inverse linear problems
CARUSO, Noe Angelo and Alessandro MICHELANGELI
Basic information
Original name
Krylov solvability under perturbations of abstract inverse linear problems
Authors
CARUSO, Noe Angelo (36 Australia, guarantor, belonging to the institution) and Alessandro MICHELANGELI
Edition
Journal of Applied Analysis, Berlin (Germany), Walter de Gruyter GMBH, 2023, 1425-6908
Other information
Type of outcome
Článek v odborném periodiku
Field of Study
10102 Applied mathematics
Country of publisher
Germany
Confidentiality degree
není předmětem státního či obchodního tajemství
RIV identification code
RIV/47813059:19610/23:A0000131
Organization unit
Mathematical Institute in Opava
Keywords in English
Inverse linear problems; Krylov solvability; infinite-dimensional Hilbert space; Hausdorff distance; subspace perturbations; weak topology
Tags
International impact, Reviewed
V originále
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.
Displayed: 26/12/2024 12:44