@article {2018,
title = {On Krylov solutions to infinite-dimensional inverse linear problems},
number = {SISSA;49/2018/MATE},
year = {2018},
institution = {SISSA},
abstract = {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.},
url = {http://preprints.sissa.it/handle/1963/35327},
author = {Noe Caruso and Alessandro Michelangeli and Paolo Novati}
}
@article {2018,
title = {Truncation and convergence issues for bounded linear inverse problems in Hilbert space},
number = {SISSA;50/2018/MATE},
year = {2018},
institution = {SISSA},
abstract = {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.},
url = {http://preprints.sissa.it/handle/1963/35326},
author = {Noe Caruso and Alessandro Michelangeli and Paolo Novati}
}