{"product_id":"9783030881580","title":"Springer Monographs in Mathematics","description":"\u003ch1\u003eSpringer Monographs in Mathematics\u003c\/h1\u003e \u003ch2\u003eCaruso, Noè Angelo; Michelangeli, Alessandro\u003c\/h2\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\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2022-02-11\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030881580\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-88159-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 140\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":44521606119564,"sku":"9783030881580","price":107.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030881580.jpg?v=1775706224","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783030881580","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}