Ill-Posed Problems in Natural Sciences PDF Download
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Author: Andrei N. Tikhonov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112313933
Category : Mathematics
Languages : en
Pages : 608
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Book Description
No detailed description available for "Ill-Posed Problems in Natural Sciences".
Author: Andrei N. Tikhonov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112313933
Category : Mathematics
Languages : en
Pages : 608
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Book Description
No detailed description available for "Ill-Posed Problems in Natural Sciences".
Author: Andreĭ Nikolaevich Tikhonov
Publisher: Imported Publication
ISBN: 9780828537391
Category : Science
Languages : en
Pages : 344
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Book Description
Author: Mikhail Mikha_lovich Lavrent_ev
Publisher: American Mathematical Soc.
ISBN: 9780821898147
Category : Mathematics
Languages : en
Pages : 300
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Book Description
Physical formulations leading to ill-posed problems Basic concepts of the theory of ill-posed problems Analytic continuation Boundary value problems for differential equations Volterra equations Integral geometry Multidimensional inverse problems for linear differential equations
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: A. Bakushinsky
Publisher: Springer Science & Business Media
ISBN: 9401110263
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics, ofwhich the first results date back to about 30 years ago. By now, impressive results have been achieved both in the theory ofsolving ill-posed problems and in the applicationsofalgorithms using modem computers. To mention just one field, one can name the computer tomography which could not possibly have been developed without modem tools for solving ill-posed problems. When writing this book, the authors tried to define the place and role of ill posed problems in modem mathematics. In a few words, we define the theory of ill-posed problems as the theory of approximating functions with approximately given arguments in functional spaces. The difference between well-posed and ill posed problems is concerned with the fact that the latter are associated with discontinuous functions. This approach is followed by the authors throughout the whole book. We hope that the theoretical results will be of interest to researchers working in approximation theory and functional analysis. As for particular algorithms for solving ill-posed problems, the authors paid general attention to the principles ofconstructing such algorithms as the methods for approximating discontinuous functions with approximately specified arguments. In this way it proved possible to define the limits of applicability of regularization techniques.
Author: A. N. TIKHONOV
Publisher:
ISBN:
Category :
Languages : en
Pages : 344
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Book Description
Author: Valentin K. Ivanov
Publisher: Walter de Gruyter
ISBN: 3110944820
Category : Mathematics
Languages : en
Pages : 296
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Book Description
This monograph is a revised and extended version of the Russian edition from 1978. It includes the general theory of linear ill-posed problems concerning e. g. the structure of sets of uniform regularization, the theory of error estimation, and the optimality method. As a distinguishing feature the book considers ill-posed problems not only in Hilbert but also in Banach spaces. It is natural that since the appearance of the first edition considerable progress has been made in the theory of inverse and ill-posed problems as wall as in ist applications. To reflect these accomplishments the authors included additional material e. g. comments to each chapter and a list of monographs with annotations.
Author: A.N. Tikhonov
Publisher: Springer Science & Business Media
ISBN: 940158480X
Category : Mathematics
Languages : en
Pages : 257
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Book Description
Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.
Author: Per Christian Hansen
Publisher: SIAM
ISBN: 0898714036
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, tomography, seismology, astronomy, and other areas. Rank-deficient problems involve matrices that are either exactly or nearly rank deficient. Such problems often arise in connection with noise suppression and other problems where the goal is to suppress unwanted disturbances of the given measurements. Discrete ill-posed problems arise in connection with the numerical treatment of inverse problems, where one typically wants to compute information about some interior properties using exterior measurements. Examples of inverse problems are image restoration and tomography, where one needs to improve blurred images or reconstruct pictures from raw data. This book describes, in a common framework, new and existing numerical methods for the analysis and solution of rank-deficient and discrete ill-posed problems. The emphasis is on insight into the stabilizing properties of the algorithms and on the efficiency and reliability of the computations. The setting is that of numerical linear algebra rather than abstract functional analysis, and the theoretical development is complemented with numerical examples and figures that illustrate the features of the various algorithms.
Author: Heinz W. Engl
Publisher: Elsevier
ISBN: 1483272656
Category : Mathematics
Languages : en
Pages : 585
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Book Description
Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June 1986. 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 equations of the first kind. Other papers deal with applications in tomography, inverse scattering, detection of radiation sources, optics, partial differential equations, and parameter estimation problems. One paper discusses three topics on ill-posed problems, namely, the imposition of specified types of discontinuities on solutions of ill-posed problems, the use of generalized cross validation as a data based termination rule for iterative methods, and also a parameter estimation problem in reservoir modeling. Another paper investigates a statistical method to determine the truncation level in Eigen function expansions and for Fredholm equations of the first kind where the data contains some errors. Another paper examines the use of singular function expansions in the inversion of severely ill-posed problems arising in confocal scanning microscopy, particle sizing, and velocimetry. The collection can benefit many mathematicians, students, and professor of calculus, statistics, and advanced mathematics.
