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001441859 001__ 1441859
001441859 003__ OCoLC
001441859 005__ 20230309003346.0
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001441859 019__ $$a1296582515$$a1298387043$$a1299385754$$a1300430274
001441859 020__ $$a9783030881597$$q(electronic bk.)
001441859 020__ $$a3030881598$$q(electronic bk.)
001441859 020__ $$z303088158X
001441859 020__ $$z9783030881580
001441859 020__ $$a9783030881603
001441859 020__ $$a3030881601
001441859 020__ $$a9783030881610
001441859 020__ $$a303088161X
001441859 0247_ $$a10.1007/978-3-030-88159-7$$2doi
001441859 035__ $$aSP(OCoLC)1296533154
001441859 040__ $$aYDX$$beng$$cYDX$$dGW5XE$$dEBLCP$$dFIE$$dOCLCO$$dOCLCF$$dOCLCQ
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001441859 1001_ $$aCaruso, Noè Angelo,$$eauthor.
001441859 24510 $$aInverse linear problems on a Hilbert space and their Krylov solvability /$$cNoè Angelo Caruso, Alessandro Michelangeli.
001441859 260__ $$aCham, Switzerland :$$bSpringer,$$c2021.
001441859 300__ $$a1 online resource
001441859 336__ $$atext$$btxt$$2rdacontent
001441859 337__ $$acomputer$$bc$$2rdamedia
001441859 338__ $$aonline resource$$bcr$$2rdacarrier
001441859 4901_ $$aSpringer monographs in mathematics
001441859 504__ $$aIncludes bibliographical references and index.
001441859 5050_ $$aIntroduction 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.
001441859 506__ $$aAccess limited to authorized users.
001441859 520__ $$aThis 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.
001441859 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed February 25, 2022).
001441859 650_0 $$aInverse problems (Differential equations)
001441859 650_0 $$aHilbert space.
001441859 650_0 $$aLinear operators.
001441859 650_6 $$aProblèmes inverses (Équations différentielles)
001441859 650_6 $$aEspace de Hilbert.
001441859 650_6 $$aOpérateurs linéaires.
001441859 655_0 $$aElectronic books.
001441859 7001_ $$aMichelangeli, Alessandro,$$eauthor.
001441859 77608 $$iPrint version: $$z303088158X$$z9783030881580$$w(OCoLC)1265456008
001441859 830_0 $$aSpringer monographs in mathematics.
001441859 852__ $$bebk
001441859 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-88159-7$$zOnline Access$$91397441.1
001441859 909CO $$ooai:library.usi.edu:1441859$$pGLOBAL_SET
001441859 980__ $$aBIB
001441859 980__ $$aEBOOK
001441859 982__ $$aEbook
001441859 983__ $$aOnline
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