Krylov Solvability of Unbounded Inverse Linear Problems

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dc.contributor.areamathematicsen_US
dc.contributor.authorCaruso, Noè Angelo
dc.contributor.authorMichelangeli, Alessandro
dc.date.accessioned2021-02-22T10:35:07Z
dc.date.available2021-02-22T10:35:07Z
dc.date.issued2019
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.identifier.urihttps://openscience.sissa.it/handle/1963/35424
dc.language.isoenen_US
dc.subjectInverse linear problemsen_US
dc.subjectConjugate gradient methodsen_US
dc.subjectUnbounded operators on Hilbert spaceen_US
dc.subjectSelf-adjoint operatorsen_US
dc.subjectKrylov subspacesen_US
dc.subjectKrylov solutionen_US
dc.titleKrylov Solvability of Unbounded Inverse Linear Problemsen_US
dc.typeArticleen_US
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