{"product_id":"inverse-linear-problems-on-hilbert-space-and-their-krylov-solvability-paperback","title":"Inverse Linear Problems on Hilbert Space and Their Krylov Solvability - Paperback","description":"\u003cp\u003eby \u003cb\u003eNoè Angelo Caruso\u003c\/b\u003e (Author), \u003cb\u003eAlessandro Michelangeli\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector \u003ci\u003ef\u003c\/i\u003e in a Hilbert space \u003ci\u003eH\u003c\/i\u003e, a linear operator \u003ci\u003eA\u003c\/i\u003e acting on \u003ci\u003eH\u003c\/i\u003e, and a vector \u003ci\u003eg\u003c\/i\u003e in \u003ci\u003eH\u003c\/i\u003e satisfying \u003ci\u003eAf=g\u003c\/i\u003e, one is interested in approximating \u003ci\u003ef\u003c\/i\u003e by finite linear combinations of \u003ci\u003eg\u003c\/i\u003e, \u003ci\u003eAg\u003c\/i\u003e, \u003ci\u003eA\u003csup\u003e2\u003c\/sup\u003eg\u003c\/i\u003e, \u003ci\u003eA\u003csup\u003e3\u003c\/sup\u003eg\u003c\/i\u003e, ... The closed subspace generated by the latter vectors is called the Krylov subspace of \u003ci\u003eH\u003c\/i\u003e generated by \u003ci\u003eg\u003c\/i\u003e and \u003ci\u003eA\u003c\/i\u003e. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.\u003c\/p\u003e\u003cp\u003eAfter 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.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector \u003ci\u003ef\u003c\/i\u003e in a Hilbert space \u003ci\u003eH\u003c\/i\u003e, a linear operator \u003ci\u003eA\u003c\/i\u003e acting on \u003ci\u003eH\u003c\/i\u003e, and a vector \u003ci\u003eg\u003c\/i\u003e in \u003ci\u003eH\u003c\/i\u003e satisfying \u003ci\u003eAf=g\u003c\/i\u003e, one is interested in approximating \u003ci\u003ef\u003c\/i\u003e by finite linear combinations of \u003ci\u003eg\u003c\/i\u003e, \u003ci\u003eAg\u003c\/i\u003e, \u003ci\u003eA\u003csup\u003e2\u003c\/sup\u003eg\u003c\/i\u003e, \u003ci\u003eA\u003csup\u003e3\u003c\/sup\u003eg\u003c\/i\u003e, ... The closed subspace generated by the latter vectors is called the Krylov subspace of \u003ci\u003eH\u003c\/i\u003e generated by \u003ci\u003eg\u003c\/i\u003e and \u003ci\u003eA\u003c\/i\u003e. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.\u003c\/p\u003e\u003cp\u003eAfter 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.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eNoè Angelo Caruso\u003c\/b\u003e is a postdoctoral researcher at the Gran Sasso Science Institute (GSSI) in L'Aquila, and a recent PhD graduate in Mathematical Analysis, Modelling and Applications from the International School of Advanced Studies (SISSA) in Trieste. His research interests are in operator theory and abstract approximation theory, taking inspiration from topics in theoretical numerical analysis with a particular emphasis on underlying functional analytic aspects.\u003c\/p\u003e\u003cp\u003e​\u003cb\u003eAlessandro Michelangeli\u003c\/b\u003e is the Alexander von Humboldt Experienced Researcher at the Institute for Applied Mathematics and the Hausdorff Center for Mathematics, University of Bonn. After obtaining his PhD in mathematical physics from SISSA, Trieste, he was a post-doc and then assistant professor at Ludwig Maximilians University, Munich (2007-2015). He has held numerous other post-doctoral and visiting positions, including at Cambridge University, SISSA, and CIRM (Trento). His research focuses on mathematical methods in physics, and the rigorous operator-theoretic understanding of numerical algorithms. In 2017 he was awarded the Alexander Vasiliev Award for an outstanding paper published in Analysis and Mathematical Physics.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 140\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.33 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e February 11, 2023\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":47445257879730,"sku":"9783030881610","price":194.38,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0770\/3891\/1666\/files\/5467fb47833464a10c17f5cde1b3cc1a.webp?v=1778718695","url":"https:\/\/box.dadyminds.org\/products\/inverse-linear-problems-on-hilbert-space-and-their-krylov-solvability-paperback","provider":"DADYMINDS BOX","version":"1.0","type":"link"}