Browsing by Author "Novati, Paolo"

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    On Krylov solutions to infinite-dimensional inverse linear problems
    (SISSA, 2018-11) Caruso, Noe; Michelangeli, Alessandro; Novati, Paolo; Mathematics
    We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of the considered inverse problem. The presentation is based on theoretical results together with a series of model examples, and it is corroborated by specific numerical experiments.
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    Truncation and convergence issues for bounded linear inverse problems in Hilbert space
    (SISSA, 2018) Caruso, Noe; Michelangeli, Alessandro; Novati, Paolo; Mathematics
    We present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests.