{"product_id":"inverse-linear-problems-on-hilbert-no-angelo-caruso-9783030881610","title":"Inverse Linear Problems on Hilbert Space and Their Krylov Solvability","description":"\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\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Noè Angelo Caruso, Alessandro Michelangeli\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 303088161X\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783030881610\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 02\/11\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 140\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.50lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.33d","brand":"Noè Angelo Caruso","offers":[{"title":"Paperback","offer_id":44131732095231,"sku":"9783030881610","price":119.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_fd5bc333-a473-4e21-b220-4c3efaf79672.jpg?v=1687476081","url":"https:\/\/www.whiterainbookhouse.com\/products\/inverse-linear-problems-on-hilbert-no-angelo-caruso-9783030881610","provider":"WR Book House","version":"1.0","type":"link"}