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Titlebook: Surveys on Solution Methods for Inverse Problems; David Colton,Heinz W. Engl,William Rundell Book 2000 Springer-Verlag Wien 2000 Ill-posed

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书目名称Surveys on Solution Methods for Inverse Problems
编辑David Colton,Heinz W. Engl,William Rundell
视频video
概述Invited survey papers by leading experts.One of the central fields in applied mathematics.Numerical solution is very difficult
图书封面Titlebook: Surveys on Solution Methods for Inverse Problems;  David Colton,Heinz W. Engl,William Rundell Book 2000 Springer-Verlag Wien 2000 Ill-posed
描述Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods". This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.
出版日期Book 2000
关键词Ill-posed problems; geophysics; image processing; inverse scattering theory; regularization methods; scat
版次1
doihttps://doi.org/10.1007/978-3-7091-6296-5
isbn_softcover978-3-211-83470-1
isbn_ebook978-3-7091-6296-5
copyrightSpringer-Verlag Wien 2000
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Iterative Regularization Techniques in Image Reconstruction,. We present a number of preconditioners for the minimization of the corresponding Tikhonov functional, and discuss the alternative of terminating the iteration early, rather than adding a stabilizing term in the Tikhonov functional. The methods are examplified for a (synthetic) model problem.
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Carleman Estimates and Inverse Problems in the Last Two Decades,lems. Since 1981 this tool has been applied to inverse problems for PDEs. The goal of this paper is to provide a tutorial-like short review of the role which Carleman estimates play in three fundamental issues of inverse problems: uniqueness, stability, and numerical methods.
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