2021/04/16 by Noè Angelo Caruso, Caruso, Noe Angelo, Alessandro Michelangeli +1
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2104.08133
openalex publication_date 2021/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.