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＜電子ブック＞
Inverse Linear Problems on Hilbert Space and their Krylov Solvability / by Noè Angelo Caruso, Alessandro Michelangeli
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	XI, 140 p. 8 illus. in color : online resource
著者標目	*Caruso, Noè Angelo author Michelangeli, Alessandro author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Functional analysis LCSH:Numerical analysis LCSH:Operator theory FREE:Differential Equations FREE:Functional Analysis FREE:Numerical Analysis FREE:Operator Theory
一般注記	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 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. HTTP:URL=https://doi.org/10.1007/978-3-030-88159-7

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