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Krilov solvability of unbounded inverse linear problems

Show simple item record Caruso, Noe Michelangeli, Alessandro 2020-01-23T07:37:33Z 2020-01-23T07:37:33Z 2020-01-23
dc.description 21 p. en_US
dc.description.abstract The abstract issue of ‘Krylov solvability’ is extensively discussed for the inverse problem Af = g where A is a (possibly unbounded) linear operator on an infinite-dimensional Hilbert space, and g is a datum in the range of A. The question consists of whether the solution f can be approximated in the Hilbert norm by finite linear combinations of g, Ag, A2g, . . . , and whether solutions of this sort exist and are unique. After revisiting the known picture when A is bounded, we study the general case of a densely defined and closed A. Intrinsic operator-theoretic mechanisms are identified that guarantee or prevent Krylov solvability, with new features arising due to the unboundedness. Such mechanisms are checked in the self-adjoint case, where Krylov solvability is also proved by conjugate-gradient-based techniques en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries SISSA;25/2019/MATE
dc.subject inverse linear problems en_US
dc.subject conjugate gradient methods en_US
dc.subject unbounded operators on Hilbert space en_US
dc.subject self-adjoint operators en_US
dc.subject Krylov subspaces en_US
dc.subject Krylov solution en_US
dc.title Krilov solvability of unbounded inverse linear problems en_US
dc.type Preprint en_US

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