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Titlebook: Inverse Problems; Basics, Theory and A Mathias Richter Textbook 20161st edition Springer International Publishing AG 2016 inverse problems.

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发表于 2025-3-21 19:54:24 | 显示全部楼层 |阅读模式
书目名称Inverse Problems
副标题Basics, Theory and A
编辑Mathias Richter
视频videohttp://file.papertrans.cn/475/474678/474678.mp4
概述Provides practical guidelines for actual numerical solution of concrete problems.Offers many detailed examples of practical interest from geophysics.Features mathematical theory on a level accessible
丛书名称Lecture Notes in Geosystems Mathematics and Computing
图书封面Titlebook: Inverse Problems; Basics, Theory and A Mathias Richter Textbook 20161st edition Springer International Publishing AG 2016 inverse problems.
描述.The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B..A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography.. .The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level..
出版日期Textbook 20161st edition
关键词inverse problems; Ill-posed problems; regularization; geomathematics; seismic tomography; inverse gravime
版次1
doihttps://doi.org/10.1007/978-3-319-48384-9
isbn_ebook978-3-319-48384-9Series ISSN 2730-5996 Series E-ISSN 2512-3211
issn_series 2730-5996
copyrightSpringer International Publishing AG 2016
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发表于 2025-3-21 20:50:59 | 显示全部楼层
Discretization of Inverse Problems, even the equation .(.) = . itself is perfectly known, if . is a function. Rather, an approximation of . has to be constructed on the basis of a finite number of (inexact) measurements (observations).
发表于 2025-3-22 02:20:37 | 显示全部楼层
Regularization of Nonlinear Inverse Problems,to our nonlinear model problems (Sects. 4.2, 4.5, and 4.6). Nonlinear Tikhonov regularization leads to nonlinear least squares problems. Sections 4.3 and 4.4 present algorithms to solve these numerically.
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Regularization of Linear Inverse Problems,iably, but whether its solution is of any relevance depends on how the replacement problem was constructed. We will especially consider Tikhonov regularization and iterative regularization methods. The following discussion is restricted to the Euclidean space over the field of real numbers ., but could easily be extended to complex spaces.
发表于 2025-3-22 18:18:49 | 显示全部楼层
Springer International Publishing AG 2016
发表于 2025-3-22 23:28:33 | 显示全部楼层
Inverse Problems978-3-319-48384-9Series ISSN 2730-5996 Series E-ISSN 2512-3211
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Lecture Notes in Geosystems Mathematics and Computinghttp://image.papertrans.cn/i/image/474678.jpg
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