Numerical Treatment Of Inverse Problems In Differential And Integral Equations
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Numerical Treatment Of Inverse Problems In Differential And Integral Equations
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Author : Deuflhard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Treatment Of Inverse Problems In Differential And Integral Equations written by Deuflhard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In many scientific or engineering applications, where ordinary differen tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given meas ured data and an associated theoretical model, determine unknown para meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "discrepancy" between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the sen sitivity coefficients for the model. may be rather time and storage con suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inev itable discretization errors, regularization techniques are necessary.
Numerical Treatment Of Inverse Problems In Differential And Integral Equations
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Author : 3Island Press
language : en
Publisher:
Release Date : 1983-01-01
Numerical Treatment Of Inverse Problems In Differential And Integral Equations written by 3Island Press and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with categories.
Numerical Treatment Of Inverse Problems In Differential And Integral Equations
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Author : Peter Deuflhard
language : en
Publisher:
Release Date : 1983
Numerical Treatment Of Inverse Problems In Differential And Integral Equations written by Peter Deuflhard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Numerical Treatment Of Inverse Problems In Differential And Integral Equations
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Author : Peter Deuflhard
language : en
Publisher:
Release Date : 1983
Numerical Treatment Of Inverse Problems In Differential And Integral Equations written by Peter Deuflhard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Inverse Problems In The Mathematical Sciences
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Author : Charles W. Groetsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-14
Inverse Problems In The Mathematical Sciences written by Charles W. Groetsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-14 with Technology & Engineering categories.
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.
Inverse Problems For Maxwell S Equations
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Author : V. Vladimir Gavrilovich Romanov
language : en
Publisher: VSP
Release Date : 1994
Inverse Problems For Maxwell S Equations written by V. Vladimir Gavrilovich Romanov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
The book offers a simultaneous presentation of the theory and numerical treatment of inverse problems for Maxwell's equations. The inverse problems are central to many areas of science and technology such as geophysical exploration, remote sensing, near-surface radar-location, dielectric logging, medical imaging, etc. The basic idea. of inverse methods is to extract from the evaluation of measured electromagnetic field the details of the medium considered. The inverse problems are investigated not only for Maxwell's equations but also for their guasistationary approximation and in the case of harmonic dependence in time. Starting with the simplest one-dimensional inverse problems, the book leads its readers to more complicated multidimensional ones studied for media of various kinds. The unique solvability of a number of the considered problems is shown as well as the stability of their solutions. The numerical analysis ranges from the finite-difference scheme inversion to the linearization method and finally the dynamic variant of the Gel'fand-Levitan method. Computational results are presented. The book is intended to provide graduate students in applied mathematics and geophysics, as well as the researches in the field, with an understanding of inverse problem theory. Although the main part of the book is rather theoretical in nature, it is also of practical value to experimentalists and engineers.
Introduction To Inverse Problems For Differential Equations
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Author : Alemdar Hasanov Hasanoğlu
language : en
Publisher: Springer
Release Date : 2017-07-31
Introduction To Inverse Problems For Differential Equations written by Alemdar Hasanov Hasanoğlu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-31 with Mathematics categories.
This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties.
Surveys On Solution Methods For Inverse Problems
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Author : David Colton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Surveys On Solution Methods For Inverse Problems written by David Colton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Integral Equations And Inverse Problems
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Author : Vesselin Petkov
language : en
Publisher:
Release Date : 1991
Integral Equations And Inverse Problems written by Vesselin Petkov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Inverse Problems In Partial Differential Equations
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Author : David L. Colton
language : en
Publisher: SIAM
Release Date : 1990-01-01
Inverse Problems In Partial Differential Equations written by David L. Colton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.