Numerical Treatment Of Inverse Problems In Differential Equations 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 Equations And Integral Equations
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Author : Peter Deuflhard
language : en
Publisher:
Release Date : 1983
Numerical Treatment Of Inverse Problems In Differential Equations 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.
Classical applied mathematics is dominated by the Laplacian paradigm of known causes evolving continuously into uniquely determined effects. The classical direct problem is then to find the unique effect of a given cause by using the appropriate law of evolution. It is therefore no surprise that traditional teaching in mathema tics and the natural sciences emphasizes the point of view that problems have a solution, this solution is unique, and the solution is insensitive to small changes in the problem. Such problems are called well-posed and they typically arise from the so-called direct problems of natural science. The demands of science and technology have recently brought to the fore many problems that are inverse to the classical direct problems, that is, problems which may be interpreted as finding the cause of a given effect or finding the law of evolution given the cause and effect. Included among such problems are many questions of remote sensing or indirect measurement such as the determination of internal characteristics of an inaccessible region from measurements on its boundary, the determination of system parameters from input output measurements, and the reconstruction of past events from measurements of the present state. Inverse problems of this type are often ill-posed in the sense that distinct causes can account for the same effect and small changes in a perceived effect can correspond to very large changes in a given cause. Very frequently such inverse problems are modeled by integral equations of the first kind.
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.
Inverse Problems In Differential Equations
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Author : G. Anger
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1990-12-31
Inverse Problems In Differential Equations written by G. Anger and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-31 with Mathematics categories.
No detailed description available for "Inverse Problems in Differential Equations".
Abel Integral Equations
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Author : Rudolf Gorenflo
language : en
Publisher: Springer
Release Date : 2006-11-14
Abel Integral Equations written by Rudolf Gorenflo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.
Model Reduction And Coarse Graining Approaches For Multiscale Phenomena
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Author : Alexander N. Gorban
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-22
Model Reduction And Coarse Graining Approaches For Multiscale Phenomena written by Alexander N. Gorban 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 2006-09-22 with Science categories.
Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.
An Introduction To The Mathematical Theory Of Inverse Problems
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Author : Andreas Kirsch
language : en
Publisher: Springer Nature
Release Date : 2021-02-15
An Introduction To The Mathematical Theory Of Inverse Problems written by Andreas Kirsch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-15 with Mathematics categories.
This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.
Practical Methods For Optimal Control And Estimation Using Nonlinear Programming
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Author : John T. Betts
language : en
Publisher: SIAM
Release Date : 2010-01-01
Practical Methods For Optimal Control And Estimation Using Nonlinear Programming written by John T. Betts and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
The book describes how sparse optimization methods can be combined with discretization techniques for differential-algebraic equations and used to solve optimal control and estimation problems. The interaction between optimization and integration is emphasized throughout the book.
Production Factor Mathematics
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Author : Martin Grötschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-05
Production Factor Mathematics written by Martin Grötschel 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 2010-08-05 with Mathematics categories.
Mathematics as a production factor or driving force for innovation? Those, who want to know and understand why mathematics is deeply involved in the design of products, the layout of production processes and supply chains will find this book an indispensable and rich source. Describing the interplay between mathematical and engineering sciences the book focusses on questions like How can mathematics improve to the improvement of technological processes and products? What is happening already? Where are the deficits? What can we expect for the future? 19 articles written by mixed teams of authors of engineering, industry and mathematics offer a fascinating insight of the interaction between mathematics and engineering.