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

Language

English

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

References:

Journal of Applied Analysis

RIV identification code

RIV/47813059:19610/23:A0000131

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.1515/jaa-2022-2004

UT WoS

000871701200001

Keywords in English

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

Tags

Tags

International impact, Reviewed
Změněno: 2/4/2024 13:17, Mgr. Aleš Ryšavý

Abstract

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