Mathematics

Numerical Methods for Solving Inverse Problems of Mathematical Physics

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

Publisher: Walter de Gruyter

ISBN: 3110205793

Category: Mathematics

Page: 452

View: 406

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.
Mathematics

Regularization Algorithms for Ill-Posed Problems

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

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110557355

Category: Mathematics

Page: 342

View: 8763

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
Mathematics

Inverse Problems of Mathematical Physics

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

Publisher: Walter de Gruyter

ISBN: 3110915529

Category: Mathematics

Page: 281

View: 8333

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.
Computers

Numerical Analysis and Its Applications

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

Author: Ivan Dimov,István Faragó,Lubin Vulkov

Publisher: Springer

ISBN: 3642415156

Category: Computers

Page: 572

View: 8597

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.
Mathematics

Investigation Methods for Inverse Problems

Author: Vladimir G. Romanov

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110943840

Category: Mathematics

Page: 292

View: 3880

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.
Mathematics

Inverse and Ill-Posed Sources Problems

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

Publisher: Walter de Gruyter

ISBN: 3110969416

Category: Mathematics

Page: 239

View: 9863

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.
Mathematics

Computational Methods for Applied Inverse Problems

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

Publisher: Walter de Gruyter

ISBN: 3110259052

Category: Mathematics

Page: 550

View: 3727

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.
Mathematics

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

Author: Petrov Yuri P.,Valery S. Sizikov

Publisher: Walter de Gruyter

ISBN: 3110195305

Category: Mathematics

Page: 240

View: 8385

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.
Mathematics

Carleman Estimates for Coefficient Inverse Problems and Numerical Applications

Author: Michael V. Klibanov,Aleksandr Anatolʹevich Timonov

Publisher: Walter de Gruyter

ISBN: 9789067644051

Category: Mathematics

Page: 282

View: 1356

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.
Mathematics

Optimal Methods for Ill-Posed Problems

With Applications to Heat Conduction

Author: Vitalii P. Tanana,Anna I. Sidikova

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110577216

Category: Mathematics

Page: 138

View: 4173

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
Mathematics

Inverse and Ill-posed Problems

Theory and Applications

Author: Sergey I. Kabanikhin

Publisher: Walter de Gruyter

ISBN: 3110224011

Category: Mathematics

Page: 475

View: 1208

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.
Mathematics

Operator Theory and Ill-Posed Problems

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

Publisher: Walter de Gruyter

ISBN: 3110960729

Category: Mathematics

Page: 696

View: 1246

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.
Mathematics

Optimal Methods for Ill-Posed Problems

With Applications to Heat Conduction

Author: Vitalii P. Tanana,Anna I. Sidikova

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110577216

Category: Mathematics

Page: 138

View: 634

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
Science

Ill-Posed and Inverse Problems

Dedicated to Academician Mikhail Mikhailovich Laverentiev on the Occasion of His 70th Birthday

Author: Vladimir G. Romanov,S. I. Kabanikhin,A. L. Bukhgeim

Publisher: VSP

ISBN: 9789067643627

Category: Science

Page: 468

View: 5958

M.M. Lavrentiev is the author of many fundamental scientific results in many directions of mathematics and its applications, such as differential equations, inverse and ill-posed problems, tomography, numerical and applied mathematics. His results in the theory of inverse problems for differential equations and in tomography are well known all over the world. To honour him on the occasion of his 70th birthday renowned scientists in this field of mathematics, both from East and West, have contributed to this special collection of papers on ill-posed and inverse problems, which will be of interest to anyone working in this field.
Mathematics

Ill-Posed Problems with A Priori Information

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

Publisher: Walter de Gruyter

ISBN: 3110900114

Category: Mathematics

Page: 264

View: 9743

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.
Mathematics

Nonlinear and Inverse Problems in Electromagnetics

PIERS 2017, St. Petersburg, Russia, May 22-25

Author: L. Beilina,Yu. G. Smirnov

Publisher: Springer

ISBN: 3319940600

Category: Mathematics

Page: 145

View: 849

This volume provides academic discussion on the theory and practice of mathematical analysis of nonlinear and inverse problems in electromagnetics and their applications. From mathematical problem statement to numerical results, the featured articles provide a concise overview of comprehensive approaches to the solution of problems. Articles highlight the most recent research concerning reliable theoretical approaches and numerical techniques and cover a wide range of applications, including acoustics, electromagnetics, optics, medical imaging, and geophysics. The nonlinear and ill-posed nature of inverse problems and the challenges they present when developing new numerical methods are explained, and numerical verification of proposed new methods on simulated and experimental data is provided. Based on the special session of the same name at the 2017 Progress in Electromagnetics Research Symposium, this book offers a platform for interaction between theoretical and practical researchers and between senior and incoming members in the field.
Mathematics

The Mollification Method and the Numerical Solution of Ill-Posed Problems

Author: Diego A. Murio

Publisher: John Wiley & Sons

ISBN: 1118031466

Category: Mathematics

Page: 272

View: 6395

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.
Mathematics

Numerical Methods for the Solution of Ill-Posed Problems

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

Publisher: Springer Science & Business Media

ISBN: 940158480X

Category: Mathematics

Page: 254

View: 5429

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.
Inverse problems (Differential equations)

Discrete Inverse Problems

Insight and Algorithms

Author: Per Christian Hansen

Publisher: SIAM

ISBN: 089871883X

Category: Inverse problems (Differential equations)

Page: 213

View: 7858

This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.