| 书目名称 | Inverse Linear Problems on Hilbert Space and their Krylov Solvability |
| 编辑 | Noè Angelo Caruso,Alessandro Michelangeli |
| 视频video | |
| 概述 | Gives a detailed presentation of the theory of abstract inverse linear problems on Hilbert space.Provides the first comprehensive analysis of Krylov solvability.Includes a multitude of novel results p |
| 丛书名称 | Springer Monographs in Mathematics |
| 图书封面 |  |
| 描述 | .This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector .f. in a Hilbert space .H., a linear operator .A. acting on .H., and a vector .g. in .H. satisfying .Af=g., one is interested in approximating .f. by finite linear combinations of .g., .Ag., .A.2.g., .A.3.g., … The closed subspace generated by the latter vectors is called the Krylov subspace of .H. generated by .g. and .A.. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text..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..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 researche |
| 出版日期 | Book 2021 |
| 关键词 | inverse linear problems on Hilbert space; infinite-dimensional Hilbert space; ill-posed problems; ortho |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-88159-7 |
| isbn_softcover | 978-3-030-88161-0 |
| isbn_ebook | 978-3-030-88159-7Series ISSN 1439-7382 Series E-ISSN 2196-9922 |
| issn_series | 1439-7382 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 19:08:18
