| 书目名称 | Nonlinear Least Squares for Inverse Problems | | 副标题 | Theoretical Foundati | | 编辑 | Guy Chavent | | 视频video | | | 概述 | Step-by-step guide to solving Nonlinear Inverse Problems with Least Square methods.Contains a geometric theory to analyze Wellposedness and Optimizability.Detailed analysis of practical issues when so | | 丛书名称 | Scientific Computation | | 图书封面 |  | | 描述 | The domain of inverse problems has experienced a rapid expansion, driven by the increase in computing power and the progress in numerical modeling. When I started working on this domain years ago, I became somehow fr- tratedtoseethatmyfriendsworkingonmodelingwhereproducingexistence, uniqueness, and stability results for the solution of their equations, but that I was most of the time limited, because of the nonlinearity of the problem, to provethatmyleastsquaresobjectivefunctionwasdi?erentiable....Butwith my experience growing, I became convinced that, after the inverse problem has been properly trimmed, the ?nal least squares problem, the one solved on the computer, should be Quadratically (Q)-wellposed,thatis,both we- posed and optimizable: optimizability ensures that a global minimizer of the least squares function can actually be found using e?cient local optimization algorithms, and wellposedness that this minimizer is stable with respect to perturbation of the data. But the vast majority of inverse problems are nonlinear, and the clas- cal mathematical tools available for their analysis fail to bring answers to these crucial questions: for example, compactness will ensure exi | | 出版日期 | Book 2010 | | 关键词 | analysis of NLS problems; analysis of nonlinear least square problems; choice of parametrization; inver | | 版次 | 1 | | doi | https://doi.org/10.1007/978-90-481-2785-6 | | isbn_softcover | 978-94-007-3060-1 | | isbn_ebook | 978-90-481-2785-6Series ISSN 1434-8322 Series E-ISSN 2198-2589 | | issn_series | 1434-8322 | | copyright | Springer Science+Business Media B.V. 2010 |
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发表于 2025-3-21 18:19:02
