{"product_id":"inverse-linear-problems-on-hilbert-space-and-their-krylov-solvability-von-noe-angelo-caruso-und-alessandro-michelangeli","title":"Inverse Linear Problems on Hilbert Space and their Krylov Solvability","description":"\n                                \n                \u003cp\u003e\n                                        This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector \n                    \n                    \u003ci\u003ef\u003c\/i\u003e\n                                         in a Hilbert space \n                    \n                    \u003ci\u003eH\u003c\/i\u003e\n                                        , a linear operator \n                    \n                    \u003ci\u003eA\u003c\/i\u003e\n                                         acting on \n                    \n                    \u003ci\u003eH\u003c\/i\u003e\n                                        , and a vector \n                    \n                    \u003ci\u003eg\u003c\/i\u003e\n                                         in \n                    \n                    \u003ci\u003eH\u003c\/i\u003e\n                                         satisfying \n                    \n                    \u003ci\u003eAf=g\u003c\/i\u003e\n                                        , one is interested in approximating \n                    \n                    \u003ci\u003ef\u003c\/i\u003e\n                                         by finite linear combinations of \n                    \n                    \u003ci\u003eg\u003c\/i\u003e\n                                        , \n                    \n                    \u003ci\u003eAg\u003c\/i\u003e\n                                        , \n                    \n                    \u003ci\u003e\n                                                A\n                        \n                        \u003csup\u003e2\u003c\/sup\u003e\n                                                g\n                    \n                    \u003c\/i\u003e\n                                        , \n                    \n                    \u003ci\u003e\n                                                A\n                        \n                        \u003csup\u003e3\u003c\/sup\u003e\n                                                g\n                    \n                    \u003c\/i\u003e\n                                        , … The closed subspace generated by the latter vectors is called the Krylov subspace of \n                    \n                    \u003ci\u003eH\u003c\/i\u003e\n                                         generated by \n                    \n                    \u003ci\u003eg\u003c\/i\u003e\n                                         and \n                    \n                    \u003ci\u003eA\u003c\/i\u003e\n                                        . The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.\n                \n                \u003c\/p\u003e\n                                \n                \u003cp\u003e\n                                        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.\n                    \n                    \u003cbr\u003e\n                                    \n                \u003c\/p\u003e\n                                \n                \u003cp\u003e\n                                        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.\n                    \n                    \u003cbr\u003e\n                                    \n                \u003c\/p\u003e\n                                \n                \u003cp\u003e \u003c\/p\u003e\n                                \n                \u003cp\u003e\n                                        \n                    \u003cbr\u003e\n                                    \n                \u003c\/p\u003e\n                                \n                \u003cp\u003e\u003c\/p\u003e\n                            \n            \u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783030881610\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783030881580\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783030881610","offer_id":40922810679389,"sku":"9783030881610","price":117.69,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783030881580","offer_id":39822285701213,"sku":"9783030881580","price":117.69,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/d8a98f6e-d8da-41bf-a7f9-74602273749d.jpg?v=1772170293","url":"https:\/\/shop.autorenwelt.de\/en\/products\/inverse-linear-problems-on-hilbert-space-and-their-krylov-solvability-von-noe-angelo-caruso-und-alessandro-michelangeli","provider":"Autorenwelt Shop","version":"1.0","type":"link"}