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Author : G. Haemmerlin
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.:/5 (859 download)
Download or read book Improperly. Posed Problems and Their Numerical Treatment written by G. Haemmerlin and published by . This book was released on 1983 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Prof. Dr. G. Hämmerlin
Publisher : Birkhäuser
ISBN 13 : 3034854609
Total Pages : 254 pages
Book Rating : 4.0/5 (348 download)
Download or read book Improperly Posed Problems and Their Numerical Treatment written by Prof. Dr. G. Hämmerlin and published by Birkhäuser. This book was released on 2013-11-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whilst improperly posed problems appear in several branches of applied and pure mathematics, this conference concentrated mainly on the practical treatment of ill posedness. The participants came from 12 countries. The interchange of ideas reflected the spectrum of questions arising in connection with the subject of the conference, where currently progresses in research are made. This volume contains 17 papers presented at the con ference. Focal points in the programme were: Problems of regularisation, parameter identification, free boundary and inverse problems in differential equations and inte gral equations of the first kind. Problems, which appear in science, in technical fields and in medicine are dis cussed as well as general operator equations. In a jOint discussion, several open problems have been worked out which are collected at the end of the volume. The editor's thanks go to all contributors and parti cipants who made the conference a success; to the manage ment of the institute with its unique atmosphere; to the Birkhauser Verlag for the possibility to publish the vo lume in the well-known ISNM series; to Dr. P. Jochum (Mlin chen) for assistance in organization and to Mrs. Chr. Rogg (Augsburg) for her excellent typing of several manuscripts.
Author : V.A. Morozov
Publisher : Springer Science & Business Media
ISBN 13 : 1461252806
Total Pages : 275 pages
Book Rating : 4.4/5 (612 download)
Download or read book Methods for Solving Incorrectly Posed Problems written by V.A. Morozov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f € F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D , in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides with A F ("sol vabi li ty" condition); (2) The equality AU = AU for any u ,u € DA implies the I 2 l 2 equality u = u ("uniqueness" condition); l 2 (3) The inverse operator A-I is continuous on F ("stability" condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any "ill-posed" (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation.
Author : Diego A. Murio
Publisher : John Wiley & Sons
ISBN 13 : 1118031466
Total Pages : 272 pages
Book Rating : 4.1/5 (18 download)
Download or read book The Mollification Method and the Numerical Solution of Ill-Posed Problems written by Diego A. Murio and published by John Wiley & Sons. This book was released on 2011-03-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uses a strong computational and truly interdisciplinary treatment to introduce applied inverse theory. The author created the Mollification Method as a means of dealing with ill-posed problems. Although the presentation focuses on problems with origins in mechanical engineering, many of the ideas and techniques can be easily applied to a broad range of situations.
Author : Charles W. Groetsch
Publisher : Springer Science & Business Media
ISBN 13 : 3322992020
Total Pages : 154 pages
Book Rating : 4.3/5 (229 download)
Download or read book Inverse Problems in the Mathematical Sciences written by Charles W. Groetsch and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book are: causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.
Author : L. E. Payne
Publisher : SIAM
ISBN 13 : 9781611970463
Total Pages : 81 pages
Book Rating : 4.9/5 (74 download)
Download or read book Improperly Posed Problems in Partial Differential Equations written by L. E. Payne and published by SIAM. This book was released on 1975-01-01 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: Improperly posed Cauchy problems are the primary topics in this discussion which assumes that the geometry and coefficients of the equations are known precisely. Appropriate references are made to other classes of improperly posed problems. The contents include straight forward examples of methods eigenfunction, quasireversibility, logarithmic convexity, Lagrange identity, and weighted energy used in treating improperly posed Cauchy problems. The Cauchy problem for a class of second order operator equations is examined as is the question of determining explicit stability inequalities for solving the Cauchy problem for elliptic equations. Among other things, an example with improperly posed perturbed and unperturbed problems is discussed and concavity methods are used to investigate finite escape time for classes of operator equations.
Author : Willi Freeden
Publisher : Springer Science & Business Media
ISBN 13 : 364201545X
Total Pages : 1371 pages
Book Rating : 4.6/5 (42 download)
Download or read book Handbook of Geomathematics written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2010-08-13 with total page 1371 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
Author : A. Bakushinsky
Publisher : Springer Science & Business Media
ISBN 13 : 9401110263
Total Pages : 268 pages
Book Rating : 4.4/5 (11 download)
Download or read book Ill-Posed Problems: Theory and Applications written by A. Bakushinsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : George Anastassiou
Publisher : CRC Press
ISBN 13 : 0429525117
Total Pages : 413 pages
Book Rating : 4.4/5 (295 download)
Download or read book Handbook of Analytic Computational Methods in Applied Mathematics written by George Anastassiou and published by CRC Press. This book was released on 2019-06-03 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f
Author : G. Hämmerlin
Publisher : Birkhäuser
ISBN 13 : 3034893175
Total Pages : 282 pages
Book Rating : 4.0/5 (348 download)
Download or read book Constructive Methods for the Practical Treatment of Integral Equations written by G. Hämmerlin and published by Birkhäuser. This book was released on 2013-03-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: O I 1 -1 durch die GauB-Quadraturformel Q I n n L w 0 f (x 0) - i=1 1 1 Sei Rn : = I - Q das Fehlerfunktional. n Izl1, Fur eine im Kreis Kr I Kr : = {z E a: holomorphe Funktion f, f(z) = L i=O sei f i i - = x . (1. 1) : = sup{ I a 0 I r i E:JN und R (qo) * O}, qo (x) o 1 n 1 1 In Xr := {f: f holomorph in Kr und Iflr
Author : N. M. Chuong
Publisher : World Scientific
ISBN 13 : 981238944X
Total Pages : 579 pages
Book Rating : 4.8/5 (123 download)
Download or read book Abstract and Applied Analysis written by N. M. Chuong and published by World Scientific. This book was released on 2004 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material ? the coefficients may jump from domain to domain; Stochastic Analysis ? many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences
Author : N.E. Hurt
Publisher : Springer Science & Business Media
ISBN 13 : 9780792302100
Total Pages : 330 pages
Book Rating : 4.3/5 (21 download)
Download or read book Phase Retrieval and Zero Crossings written by N.E. Hurt and published by Springer Science & Business Media. This book was released on 1989-04-30 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with signal reconstruction from incomplete, noisy data. Two aspects in particular are considered: phase retrieval, which originated in x-ray crystallography and astronomical interferometry; and the problem of signal recovery from zero crossings. Also explores the differences in mathematical re
Author : Rainer Kress
Publisher : Springer Science & Business Media
ISBN 13 : 3642971466
Total Pages : 311 pages
Book Rating : 4.6/5 (429 download)
Download or read book Linear Integral Equations written by Rainer Kress and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: I fell in love with integral equations about twenty years ago when I was working on my thesis, and I am still attracted by their mathematical beauty. This book will try to stimulate the reader to share this love with me. Having taught integral equations a number of times I felt a lack of a text which adequately combines theory, applications and numerical methods. Therefore, in this book I intend to cover each of these fields with the same weight. The first part provides the basic Riesz-Fredholm theory for equa tions of the second kind with compact opertors in dual systems including all functional analytic concepts necessary for developing this theory. The second part then illustrates the classical applications of integral equation methods to boundary value problems for the Laplace and the heat equation as one of the main historical sources for the development of integral equations, and also in troduces Cauchy type singular integral equations. The third part is devoted to describing the fundamental ideas for the numerical solution of integral equa tions. Finally, in a fourth part, ill-posed integral equations of the first kind and their regularization are studied in a Hilbert space setting. In order to make the book accessible not only to mathematicans but also to physicists and engineers I have planned it as self-contained as possible by requiring only a solid foundation in differential and integral calculus and, for parts of the book, in complex function theory.
Author : Peter W. Hawkes
Publisher : Elsevier
ISBN 13 : 0080493254
Total Pages : 565 pages
Book Rating : 4.0/5 (84 download)
Download or read book Advances in Imaging and Electron Physics written by Peter W. Hawkes and published by Elsevier. This book was released on 2003-12-02 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subjects reviewed in the 'Advances' series cover a broad range of themes including microscopy, electromagnetic fields and image coding. Volume 128 concentrates on regularization, a vital aspect of restoration on low voltage scanning electron microscopy. This Book looks at theory and it's application in a practical sense, with a full account of the methods used and realistic detailed application. The authors do this by examining the latest developments, historic illustrations and mathematical fundamentals of the exciting developments in imaging and applying them to realistic practical situations The text bridges the gap between academic researchers and R&D designers by addressing and solving daily issues, which makes this book essential reading. · Emphasizes broad and in depth article collaborations between world-renowned scientists in the field of image and electron physics · Presents theory and it's application in a practical sense, providing long awaited solutions and new findings · Bridges the gap between academic researchers and practitioners in industry
Author : Giorgio Talenti
Publisher : Springer
ISBN 13 : 354047353X
Total Pages : 214 pages
Book Rating : 4.5/5 (44 download)
Download or read book Inverse Problems written by Giorgio Talenti and published by Springer. This book was released on 2006-11-14 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 1214 pages
Book Rating : 4.3/5 (91 download)
Download or read book Transactions of the ... Army Conference on Applied Mathematics and Computing written by and published by . This book was released on 1983 with total page 1214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Willi Freeden
Publisher : American Mathematical Society
ISBN 13 : 1470473453
Total Pages : 505 pages
Book Rating : 4.4/5 (74 download)
Download or read book Recovery Methodologies: Regularization and Sampling written by Willi Freeden and published by American Mathematical Society. This book was released on 2023-08-21 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.
