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arXiv · 2104.08133

Inverse linear problems on Hilbert space and their Krylov solvability

Noe Angelo Caruso·Alessandro Michelangeli
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Abstract

This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general infinite-dimensional Hilbert space; the notion of Krylov subspace associated to an inverse problem, i.e., the cyclic subspace built upon the datum of the inverse problem by repeated application of the linear operator; the possibility to solve the inverse problem by means of Krylov subspace methods, namely projection methods where the finite-dimensional truncation is made with respect to the Krylov subspace and the approximants converge to an exact solution to the inverse problem.

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BibTeXRIS

Noe Angelo Caruso, Alessandro Michelangeli. 2021-04-16. Inverse linear problems on Hilbert space and their Krylov solvability. https://arxiv.org/abs/2104.08133

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