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Truncation and convergence issues for bounded linear inverse problems in Hilbert space

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dc.contributor.author Caruso, Noe
dc.contributor.author Michelangeli, Alessandro
dc.contributor.author Novati, Paolo
dc.date.accessioned 2018-11-20T13:02:23Z
dc.date.available 2018-11-20T13:02:23Z
dc.date.issued 2018
dc.identifier.uri http://preprints.sissa.it/handle/1963/35326
dc.description.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. en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries SISSA;50/2018/MATE
dc.subject inverse linear problems en_US
dc.subject in nite-dimensional Hilbert space en_US
dc.subject ill-posed problems en_US
dc.subject orthonormal basis discretisation en_US
dc.subject bounded linear operators en_US
dc.subject Krylov subspaces en_US
dc.subject Krylov solution en_US
dc.subject GMRES en_US
dc.subject conjugate gradient en_US
dc.subject LSQR en_US
dc.title Truncation and convergence issues for bounded linear inverse problems in Hilbert space en_US
dc.type Preprint en_US
dc.miur.area 1 en_US
dc.contributor.area Mathematics en_US
dc.relation.firstpage 1 en_US
dc.relation.lastpage 25 en_US

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