Krylov solvability under perturbations of abstract inverse linear problems

@article{65301,
   author = {Caruso, Noe Angelo and Michelangeli, Alessandro},
   article_location = {Berlin (Germany)},
   article_number = {1},
   doi = {http://dx.doi.org/10.1515/jaa-2022-2004},
   keywords = {Inverse linear problems; Krylov solvability; infinite-dimensional Hilbert space; Hausdorff distance; subspace perturbations; weak topology},
   language = {eng},
   issn = {1425-6908},
   journal = {Journal of Applied Analysis},
   title = {Krylov solvability under perturbations of abstract inverse linear problems},
   url = {https://www.degruyter.com/document/doi/10.1515/jaa-2022-2004/html},
   volume = {29},
   year = {2023}
}

TY  - JOUR
ID  - 65301
AU  - Caruso, Noe Angelo - Michelangeli, Alessandro
PY  - 2023
TI  - Krylov solvability under perturbations of abstract inverse linear problems
JF  - Journal of Applied Analysis
VL  - 29
IS  - 1
SP  - 3-29
EP  - 3-29
PB  - Walter de Gruyter GMBH
SN  - 14256908
KW  - Inverse linear problems
KW  - Krylov solvability
KW  - infinite-dimensional Hilbert space
KW  - Hausdorff distance
KW  - subspace perturbations
KW  - weak topology
UR  - https://www.degruyter.com/document/doi/10.1515/jaa-2022-2004/html
N2  - 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.
ER  - 

CARUSO, Noe Angelo and Alessandro MICHELANGELI. Krylov solvability under perturbations of abstract inverse linear problems. \textit{Journal of Applied Analysis}. Berlin (Germany): Walter de Gruyter GMBH, 2023, vol.~29, No~1, p.~3-29. ISSN~1425-6908. Available from: https://dx.doi.org/10.1515/jaa-2022-2004.