Numerical Methods for Solving Inverse Problems of Mathematical Physics

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Author: A. A. Samarskii,Petr N. Vabishchevich

Publisher: Walter de Gruyter

ISBN: 3110205793

Category: Mathematics

Page: 452

View: 2199

The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

Carleman Estimates for Coefficient Inverse Problems and Numerical Applications

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Author: Michael V. Klibanov,Aleksandr Anatolʹevich Timonov

Publisher: Walter de Gruyter

ISBN: 9789067644051

Category: Mathematics

Page: 282

View: 7860

This is the first book dedicated to applying the Carleman estimates to coefficient inverse problems. Written in a readable and concise manner, the book introduces the reader to the essence of the method of Carleman estimates, which is one of the most powerful tools for the mathematical treatment of coefficient inverse problems. The core of the book is two most recent advances of the authors. These are the global uniqueness of a multidimensional coefficient inverse problem for a nonlinear parabolic equation and the so-called convexification framework for constructing globally convergent algorithms for a broad class of inverse problems. Several applications of the convexification to magnetotelluric frequency sounding, electrical impedance tomography, infra-red optical sensing of biotissies, and time reversal are considered.

Inverse and Ill-posed Problems

Theory and Applications

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Author: Sergey I. Kabanikhin

Publisher: Walter de Gruyter

ISBN: 3110224011

Category: Mathematics

Page: 475

View: 4135

The text demonstrates the methods for proving the existence (if at all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included.

Operator Theory and Ill-Posed Problems

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Author: Mikhail M. Lavrent'ev,Lev Ja. Savel'ev

Publisher: Walter de Gruyter

ISBN: 3110960729

Category: Mathematics

Page: 696

View: 6341

This book consists of three major parts. The first two parts deal with general mathematical concepts and certain areas of operator theory. The third part is devoted to ill-posed problems. It can be read independently of the first two parts and presents a good example of applying the methods of calculus and functional analysis. The first part "Basic Concepts" briefly introduces the language of set theory and concepts of abstract, linear and multilinear algebra. Also introduced are the language of topology and fundamental concepts of calculus: the limit, the differential, and the integral. A special section is devoted to analysis on manifolds. The second part "Operators" describes the most important function spaces and operator classes for both linear and nonlinear operators. Different kinds of generalized functions and their transformations are considered. Elements of the theory of linear operators are presented. Spectral theory is given a special focus. The third part "Ill-Posed Problems" is devoted to problems of mathematical physics, integral and operator equations, evolution equations and problems of integral geometry. It also deals with problems of analytic continuation. Detailed coverage of the subjects and numerous examples and exercises make it possible to use the book as a textbook on some areas of calculus and functional analysis. It can also be used as a reference textbook because of the extensive scope and detailed references with comments.

Inverse and Ill-Posed Sources Problems

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Author: Yu. E. Anikonov,B. A. Bubnov,G. N. Erokhin

Publisher: Walter de Gruyter

ISBN: 3110969416

Category: Mathematics

Page: 239

View: 6301

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 publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Numerical Methods for the Solution of Ill-Posed Problems

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Author: A.N. Tikhonov,A. Goncharsky,V.V. Stepanov,Anatoly G. Yagola

Publisher: Springer Science & Business Media

ISBN: 9780792335832

Category: Mathematics

Page: 254

View: 6055

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.

Optimal Methods for Ill-Posed Problems

With Applications to Heat Conduction

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Author: Vitalii P. Tanana,Anna I. Sidikova

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110577216

Category: Mathematics

Page: 138

View: 8021

The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems

Inverse Problems of Mathematical Physics

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Author: Viatcheslav I. Priimenko,Mikhail M. Lavrent'ev,Alexander V. Avdeev

Publisher: Walter de Gruyter

ISBN: 3110915529

Category: Mathematics

Page: 281

View: 1490

This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.

Regularization Algorithms for Ill-Posed Problems

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Author: Anatoly B. Bakushinsky,Mikhail M. Kokurin,Mikhail Yu. Kokurin

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110556383

Category: Mathematics

Page: 342

View: 3760

This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems

Inverse Problems of Vibrational Spectroscopy

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Author: I. V. Kochikov

Publisher: VSP

ISBN: 9789067643047

Category: Mathematics

Page: 297

View: 9684

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 publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Iterative Methods for Ill-Posed Problems

An Introduction

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Author: Anatoly B. Bakushinsky,Mihail Yu. Kokurin,Alexandra Smirnova

Publisher: Walter de Gruyter

ISBN: 3110250659

Category: Mathematics

Page: 147

View: 7848

Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.

Ill-Posed Problems with A Priori Information

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Author: V. V. Vasin,A. L. Ageev

Publisher: Walter de Gruyter

ISBN: 3110900114

Category: Mathematics

Page: 264

View: 5996

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 publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Well-posed, Ill-posed, and Intermediate Problems with Applications

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Author: Petrov Yuri P.,Valery S. Sizikov

Publisher: Walter de Gruyter

ISBN: 3110195305

Category: Mathematics

Page: 240

View: 5013

This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples.

Inverse problems in engineering

theory and practice

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Author: Nicholas Zabaras,Engineering Foundation (U.S.),American Society of Mechanical Engineers

Publisher: Amer Society of Mechanical

ISBN: N.A

Category: Technology & Engineering

Page: 369

View: 8235

Investigation Methods for Inverse Problems

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Author: Vladimir G. Romanov

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110943840

Category: Mathematics

Page: 292

View: 2325

This monograph deals with some inverse problems of mathematical physics. It introduces new methods for studying inverse problems and gives obtained results, which are related to the conditional well posedness of the problems. The main focus lies on time-domain inverse problems for hyperbolic equations and the kinetic transport equation.

Mathematical and Numerical Aspects of Wave Propagation WAVES 2003

Proceedings of the Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyvèaskylèa, Finland, 30 June-4 July 2003

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Author: Gary Cohen,Erkki Heikkola,Patrick Joly,Pekka Neittaanmäki

Publisher: Springer Science & Business Media

ISBN: 9783540401278

Category: Computers

Page: 932

View: 6062

These proceedings include articles of the Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2003), held in Jyviiskylii, Finland, from June 30 to July 4, 2003. As in the previous five conferences in this series, its program covered a broad range of topics related to the mathematical modeling and numerical simulation of wave phenomena. Topics of specific interest included various areas of acoustics, electromagnetics, elasticity, and related optimization and inverse problems. In addition to the nine invited presentations, we selected for this confer­ ence 152 high-level papers from over 20 countries, especially from Europe. Most of them are contained in this book. They provide an extensive overview on the recent developments in the theoretical and applied wave propagation. The conference was organized by the University of Jyviiskylii and the Institut National de Recherche en Informatique et en Automatique (INRIA) in cooperation with Jyviiskylii Congresses. The editors would like to thank the organizing institutions and the in­ ternational scientific committee for their efforts in the preparation of this conference. We are also grateful to all the authors of the papers for their contributions to these proceedings. Special acknowledgment is due to Ms. Dominique Potherat, to Ms. Helene Chanut and to Ms. Marja-Leena Ranta­ lainen for their valuable assistance in the preparation of this proceedings volume. Jyviiskylii, Gary C. Cohen February 2003 Erkki H eikkola Patrick loly Pekka Neittaanmiiki Contents Part I Invited Presentations Dispersive Properties of High Order Finite Elements Mark Ainsworth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . .

Computational Methods for Applied Inverse Problems

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Author: Yanfei Wang,Anatoly G. Yagola,Changchun Yang

Publisher: Walter de Gruyter

ISBN: 3110259052

Category: Mathematics

Page: 550

View: 3818

This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. Readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.