{"product_id":"inverse-linear-problems-on-hilbert-space-and-their-krylov-solvability-9783030881610","title":"Inverse Linear Problems on Hilbert Space and their Krylov Solvability","description":"\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003e\n\u003cbr\u003eThe book discusses the theory of abstract inverse linear problems on Hilbert space, focusing on approximating unknown vectors by finite linear combinations of known vectors using projection methods on the Krylov subspace. It provides examples and counterexamples, discusses uniqueness of solutions, and explores the behaviour of Krylov subspaces under perturbations. The book is relevant to graduate students and researchers in functional analysis, operator theory, and numerical analysis. \u003c\/blockquote\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Paperback \/ softback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 140 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 11 February 2023\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Springer Nature Switzerland AG\u003cbr\u003e\u003c\/p\u003e \u003cp\u003e\u003cbr\u003eThis comprehensive book delves into the intricate realm of abstract inverse linear problems on Hilbert spaces. It begins by introducing the fundamental concepts and assumptions required for the study of these problems. The author then presents a detailed analysis of the theory, exploring various methods and techniques for approximating unknown vectors by finite linear combinations of known vectors.\u003cbr\u003e\u003cbr\u003eThe Krylov subspace, a crucial concept in this field, is introduced, representing the closed subspace generated by a given vector and a linear operator. The book discusses the possibility of solving inverse problems using projection methods on the Krylov subspace, highlighting the advantages and limitations of such approaches.\u003cbr\u003e\u003cbr\u003eExamples and counterexamples are provided to illustrate the practical applications of the theory, showcasing both Krylov-solvable and non-solvable inverse problems. The results cover uniqueness of solutions, classes of operators that induce Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations.\u003cbr\u003e\u003cbr\u003eAn appendix is included to provide additional material on weaker convergence phenomena in general projection methods, expanding the scope of the book. This subject, situated at the intersection of functional analysis\/operator theory and numerical analysis\/approximation theory, holds significant interest for graduate students and researchers in these fields.\u003cbr\u003e\u003cbr\u003eOverall, this book offers a thorough and insightful exploration of abstract inverse linear problems on Hilbert spaces, providing valuable insights and methodologies for solving these complex problems.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 244g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 235 x 155 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9783030881610\u003cbr\u003e \u003cstrong\u003eEdition number\u003c\/strong\u003e: 1st ed. 2021\u003c\/p\u003e","brand":"Noe Angelo Caruso,Alessandro Michelangeli","offers":[{"title":"Paperback \/ softback","offer_id":44304006316282,"sku":"9783030881610","price":83.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/noImage_1_ad078bc8-1f8f-4bec-ab06-09a80aec5003.jpg?v=1688020452","url":"https:\/\/shulphink.com\/products\/inverse-linear-problems-on-hilbert-space-and-their-krylov-solvability-9783030881610","provider":"Shulph Ink","version":"1.0","type":"link"}