Krylov solvability under perturbations of abstract inverse linear problems. (English) Zbl 07709524
This paper discusses an abstract linear inverse problems in Hilbert spaces, especially the approximability by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, also known as Krylov solution. Krylov subspace type methods are very efficient and popular in practice. In this interesting paper, the authors study the possible behaviors of persistence, gain, or loss of Krylov solvability under suitable small perturbations of the infinite-dimensional inverse problem, which sheds light into the the stability or instability of Krylov methods.
Reviewer: Bangti Jin (London)
MSC:
| 47N40 | Applications of operator theory in numerical analysis |
| 65J22 | Numerical solution to inverse problems in abstract spaces |
| 47B37 | Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) |
| 65J05 | General theory of numerical analysis in abstract spaces |
Keywords:
linear inverse problems; Krylov solvability; infinite-dimensional Hilbert space; Hausdorff distance; subspace perturbations; weak topologyReferences:
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