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Inverse Linear Problems on Hilbert Space and their Krylov Solvability

Af: Alessandro Michelangeli, Noe Angelo Caruso Engelsk Paperback

Inverse Linear Problems on Hilbert Space and their Krylov Solvability

Af: Alessandro Michelangeli, Noe Angelo Caruso Engelsk Paperback
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This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by finite linear combinations of g, Ag, A2g, A3g, ... The closed subspace generated by the latter vectors is called the Krylov subspace of H generated by g and A. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.

After giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods.

This subject of this book lies at the boundary of functional analysis/operator theory and numerical analysis/approximation theory and will be of interest to graduate students and researchers in any of these fields.


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This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by finite linear combinations of g, Ag, A2g, A3g, ... The closed subspace generated by the latter vectors is called the Krylov subspace of H generated by g and A. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.

After giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods.

This subject of this book lies at the boundary of functional analysis/operator theory and numerical analysis/approximation theory and will be of interest to graduate students and researchers in any of these fields.


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Produktdetaljer
Sprog: Engelsk
Sider: 140
ISBN-13: 9783030881610
Indbinding: Paperback
Udgave:
ISBN-10: 303088161X
Kategori: Funktionsanalyse og transformation
Udg. Dato: 11 feb 2023
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 11 feb 2023
Forfatter(e): Alessandro Michelangeli, Noe Angelo Caruso
Forfatter(e) Alessandro Michelangeli, Noe Angelo Caruso

Kategori Funktionsanalyse og transformation

ISBN-13 9783030881610

Sprog Engelsk

Indbinding Paperback

Sider 140

Udgave

Længde 0mm

Bredde 155mm

Højde 235mm

Udg. Dato 11 feb 2023

Oplagsdato 11 feb 2023

Forlag Springer Nature Switzerland AG

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