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Record Nr. |
UNINA9910544877303321 |
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Autore |
Noè Angelo Caruso |
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Titolo |
Inverse linear problems on a Hilbert space and their Krylov solvability / / Noè Angelo Caruso, Alessandro Michelangeli |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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Descrizione fisica |
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1 online resource (150 pages) |
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Collana |
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Springer Monographs in Mathematics |
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Disciplina |
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Soggetti |
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Hilbert space |
Problemes inversos (Equacions diferencials) |
Espais de Hilbert |
Operadors lineals |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- Contents -- Acronyms -- Chapter 1 Introduction and motivation -- 1.1 Abstract inverse linear problems on Hilbert space -- 1.2 General truncation and approximation scheme -- 1.3 Krylov subspace and Krylov solvability -- 1.4 Structure of the book -- Chapter 2 Krylov solvability of bounded linear inverse problems -- 2.1 Krylov subspace of a Hilbert space -- 2.2 Krylov reducibility and Krylov intersection -- 2.3 Krylov solutions for a bounded linear inverse problem -- 2.3.1 Krylov solvability. Examples. -- 2.3.2 General conditions for Krylov solvability: case of injectivity -- 2.3.3 Krylov reducibility and Krylov solvability -- 2.3.4 More on Krylov solutions in the lack of injectivity -- 2.4 Krylov solvability and self-adjointness -- 2.5 Special classes of Krylov solvable problems -- 2.6 Some illustrative numerical tests -- Chapter 3 An analysis of conjugate-gradient based methods with unbounded operators -- 3.1 Unbounded posi tive self-adjoint inverse problems and conjugate gradient approach -- 3.2 Set-up and main results -- 3.3 Algebraic and measure-theoretic background properties -- 3.4 Proof of CG-convergence and additional observations -- 3.5 Unbounded CG-convergence tested numerically -- |
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