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Monday, August 3, 2020 | History

3 edition of Inverse and ill-posed sources problems found in the catalog.

Inverse and ill-posed sources problems

by IНЎU. E. Anikonov

  • 288 Want to read
  • 24 Currently reading

Published by VSP in Utrecht, The Netherlands .
Written in English

    Subjects:
  • Inverse problems (Differential equations)

  • Edition Notes

    Includes bibliographical references (p. 231-239).

    StatementYu. E. Anikov, B. A. Bubnov, and G. N. Erokhin.
    SeriesInverse and ill-posed problems series
    ContributionsBubnov, B. A., Erokhin, G. N.
    The Physical Object
    Pagination239 p. :
    Number of Pages239
    ID Numbers
    Open LibraryOL18119503M
    ISBN 109067642738

    For ill-posed problems, proper regularization procedures are elaborated. This is complemented by a development of statistical methods for inversion. The aim of this Special Issue is to make a collection of papers that comprises the latest developments in mathematics (theory, numerics) of inverse and ill-posed problems. Other problems that lead to ill-posed problems in the sense described above are the Dirichlet problem for the wave equation, the non-characteristic Cauchy problem for the heat equation, the initial boundary value problem for the backwardheat equation, inverse scattering problems (), identification of parameters (coefficients) in partial.

    Rank-Deficient and Discrete Ill-Posed Problems, P.C. Hansen, SIAM Press, (This is an excellent book on discrete linear inverse problems). Linear and Nonlinear Inverse Problems with Practical Applications, Jennifer L. Müller and, Samuli Siltanen, SIAM Press, This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical .

    These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published. J. Inv. Ill-Posed Problems16 (), – DOI / JIIP Definitions and examples of inverse and ill-posed problems S. I. Kabanikhin Survey paper Abstract. The terms “inverse problems” and “ill-posed problems” have been steadily and surely gaining popularity in modern science since the middle of the 20th Size: KB.


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Inverse and ill-posed sources problems by IНЎU. E. Anikonov Download PDF EPUB FB2

Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for.

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Inverse and Ill-Posed Sources Problems (Inverse and Ill-Posed Problems) 1st Edition by Yu. Anikonov (Author), B. Bubnov (Author), G. Erokhin (Author) & ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Cited by: 8.

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers.

Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction.

We propose a classification of inverse problems according to the type of equation, unknowns and additional. Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator Book Edition: 1.

Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other. Inverse Inverse and ill-posed sources problems book ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material.

This book is the first small step in that direction. We propose Cited by: regularization of inverse problems Download regularization of inverse problems or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get regularization of inverse problems book now. This site is like a library, Use search box in the widget to get ebook that you want.

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers.

The series aims to Pages:   As the title indicates, this book is a research monograph that introduces the reader to iterative methods for ill-posed problems. The book begins with a review of Newton’s method, the Gauss-Newton method, and the method of steepest.

The book begins with four introductory chapters that introduce inverse problems, ill-posedness, discrete ill-posed inverse problems in linear algebra, and integral equations.

Each of the remaining chapters discusses a particular class of inverse problems, including problems of integral geometry, inverse scattering, and inverse problems. This chapter proposes a new methodology for solving the ill-posed linear systems.

Most of the inverse problems appearing in engineering and science are reduced into solving the ill-posed linear systems. Various numerical methods have been proposed for solving the ill-posed systems. Inverse problems are typically ill posed, as opposed to the well-posed problems usually met in mathematical modeling.

Of the three conditions for a well-posed problem suggested by Jacques Hadamard (existence, uniqueness, and stability of the solution or solutions) the condition of stability is most often violated.

Request PDF | Inverse Problems, Ill‐posed Problems | Introduction Basic example Ill-posed problem Generalized inversion Discretization and conditioning Conclusion Bibliography | Find, read. Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other.

Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose 5/5(1). One of the best definitions of early vision is that it is inverse optics-a set of computational problems that both machines and biological organisms have to solve.

While in classical optics the problem is to determine the images of physical objects, vision is confronted with the inverse problem of recovering three-dimensional shape from the light distribution in the image.

For statisticians, the book uses classic linear regression and statistical inference to introduce the framework of ill-posed inverse problems and explain statistical questions that arise in their applications.

A review of the mathematical analysis tools required for inverse problems is also included in the appendix. Because inverse problems typically involve the estimation of certain quantities based on indirect measurements, the estimation process is often ill-posed.

Regularization methods, which have been developed to deal with this ill-posedness, are carefully explained in the early chapters of Computational Methods for Inverse Problems.

Considering different settings of inverse problems of mathematical physics, both in linear and nonlinear cases, this text looks at solvability and the search for constructive methods. In general, the problems considered are multidimensional.

Effective methods for source recovery are given for sources of different nature. Problems that are not well-posed in the sense of Hadamard are termed ill-posed. Inverse problems are often ill-posed.

For example, the inverse heat equation, deducing a previous distribution of temperature from final data, is not well-posed in that the solution is highly sensitive to changes in the final data. These problems are no longer avoided and their study is an active branch of applied mathematics, but the distinctions and terminology delineating well-posed and ill-posed remains the same as when Hadamard first defined it.

2. Ill-Posed Problem. An ill posed problem is one which doesn’t meet the three Hadamard criteria for being well-posed.Regularization of ill-posed problems Uno H¨amarik University of Tartu, Estonia Content 1. Ill-posed problems (definition and examples) 2.

Regularization of ill-posed problems with noisy data 3. Parameter choice rules for exact noise level 4. Iterative methods 5.

Discretization methods 6. Lavrentiev and Tikhonov methods and modifications 7.ILL-POSED INVERSE PROBLEMS IN ECONOMICS 1. INTRODUCTION. A parameter of an econometric model is said to be identified if it is uniquely determined by the probability distribution from which the available data are sampled (hereinafter the population distribution).

In other words, a parameter is identified if -to-one or there is a one.