Inverse linear problems on a Hilbert space and their Krylov solvability / Noè Angelo Caruso, Alessandro Michelangeli.
Caruso, Noè Angelo, author.; Michelangeli, Alessandro, author.
2021
QA371
Available Online

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Title Inverse linear problems on a Hilbert space and their Krylov solvability / Noè Angelo Caruso, Alessandro Michelangeli.
Author Caruso, Noè Angelo, author.
ISBN 9783030881597 (electronic bk.)
3030881598 (electronic bk.)
303088158X
9783030881580
9783030881603
3030881601
9783030881610
303088161X
DOI https://doi.org/10.1007/978-3-030-88159-7
Publication Details Cham, Switzerland : Springer, 2021.
Language English
Description 1 online resource
Item Number 10.1007/978-3-030-88159-7 doi
Call Number QA371
Dewey Decimal Classification 515/.357
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed February 25, 2022).
Added Author Michelangeli, Alessandro, author.
Series Springer monographs in mathematics.
Available in Other Form Print version: 9783030881580
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Introduction and motivation
Krylov solvability of bounded linear inverse problems
An analysis of conjugate-gradient based methods with unbounded operators
Krylov solvability of unbounded inverse problems
Krylov solvability in a perturbative framework
Outlook on general projection methods and weaker convergence
References
Index.

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