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.