Numerical Analysis and Its Applications

5th International Conference, NAA 2012, Lozenetz, Bulgaria, June 15-20, 2012, Revised Selected Papers

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Author: Ivan Dimov,István Faragó,Lubin Vulkov

Publisher: Springer

ISBN: 3642415156

Category: Computers

Page: 572

View: 4157

This book constitutes thoroughly revised selected papers of the 5th International Conference on Numerical Analysis and Its Applications, NAA 2012, held in Lozenetz, Bulgaria, in June 2012. The 65 revised papers presented were carefully reviewed and selected from various submissions. The papers cover a broad area of topics of interest such as numerical approximation and computational geometry; numerical linear algebra and numerical solution of transcendental equation; numerical methods for differential equations; numerical stochastics, numerical modeling; and high performance scientific computing.

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

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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: 5064

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

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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 Mikhaĭlovich Lavrentʹev,Lev I︠A︡kovlevich Savelʹev

Publisher: Walter de Gruyter

ISBN: 9789067644488

Category: Mathematics

Page: 680

View: 1121

The book is based on the course of lectures on calculus and functional analysis and several special courses given by the authors at Novosibirsk State University. It also includes results of research carried out at the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. A brief introduction to the language of set theory and elements of abstract, linear, and multilinear algebra is provided. The language of topology is introduced and fundamental concepts of analysis for vector spaces and manifolds are described in detail. The most often used spaces of smooth and generalized functions, their transformations, and the classes of linear and nonlinear operators are considered. Special attention is given to spectral theory and the fixed point theorems. A brief presentation of degree theory is provided. The part devoted to ill-posed problems includes a description of partial differential equations, integral and operator equations, and problems of integral geometry.

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: 7553

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.

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: 1333

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.

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: 3786

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

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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

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: 3110557355

Category: Mathematics

Page: 342

View: 835

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

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: 6680

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.

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: 5832

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.

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: 8653

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.

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

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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: 5986

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.

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: 5145

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.

Inverse Problems

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Inverse problems (Differential equations)

Page: N.A

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