Truncation and convergence issues for bounded linear inverse problems in Hilbert space
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.
inverse linear problems, in nite-dimensional Hilbert space, ill-posed problems, orthonormal basis discretisation, bounded linear operators, Krylov subspaces, Krylov solution, GMRES, conjugate gradient, LSQR