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Author: Petrov Yuri P.
Publisher: Walter de Gruyter
ISBN: 3110195305
Category : Mathematics
Languages : en
Pages : 245
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Book Description
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.
Author: Petrov Yuri P.
Publisher: Walter de Gruyter
ISBN: 3110195305
Category : Mathematics
Languages : en
Pages : 245
Get Book Here
Book Description
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.
Author: Mikhail M. Lavrent'ev
Publisher: Walter de Gruyter
ISBN: 3110960729
Category : Mathematics
Languages : en
Pages : 697
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Book Description
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.
Author: Daniel Lesnic
Publisher: CRC Press
ISBN: 0429683251
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Driven by the advancement of industrial mathematics and the need for impact case studies, Inverse Problems with Applications in Science and Engineering thoroughly examines the state-of-the-art of some representative classes of inverse and ill-posed problems for partial differential equations (PDEs). The natural practical applications of this examination arise in heat transfer, electrostatics, porous media, acoustics, fluid and solid mechanics – all of which are addressed in this text. Features: Covers all types of PDEs — namely, elliptic (Laplace’s, Helmholtz, modified Helmholtz, biharmonic and Stokes), parabolic (heat, convection, reaction and diffusion) and hyperbolic (wave) Excellent reference for post-graduates and researchers in mathematics, engineering and any other scientific discipline that deals with inverse problems Contains both theory and numerical algorithms for solving all types of inverse and ill-posed problems
Author: Christophe Goupil
Publisher: John Wiley & Sons
ISBN: 3527413375
Category : Science
Languages : en
Pages : 362
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Book Description
Sound knowledge of the latest research results in the thermodynamics and design of thermoelectric devices, providing a solid foundation for thermoelectric element and module design in the technical development process and thus serving as an indispensable tool for any application development. The text is aimed mainly at the project developer in the field of thermoelectric technology, both in academia and industry, as well as at graduate and advanced undergraduate students. Some core sections address the specialist in the field of thermoelectric energy conversion, providing detailed discussion of key points with regard to optimization. The international team of authors with experience in thermoelectrics research represents such institutes as EnsiCaen Universite de Paris, JPL, CalTech, and the German Aerospace Center.
Author: M. Zuhair Nashed
Publisher: Elsevier
ISBN: 1483270297
Category : Mathematics
Languages : en
Pages : 1069
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Book Description
Generalized Inverses and Applications, contains the proceedings of an Advanced Seminar on Generalized Inverses and Applications held at the University of Wisconsin-Madison on October 8-10, 1973 under the auspices of the university's Mathematics Research Center. The seminar provided a forum for discussing the basic theory of generalized inverses and their applications to analysis and operator equations. Numerical analysis and approximation methods are considered, along with applications to statistics and econometrics, optimization, system theory, and operations research. Comprised of 14 chapters, this book begins by describing a unified approach to generalized inverses of linear operators, with particular reference to algebraic, topological, extremal, and proximinal properties. The reader is then introduced to the algebraic aspects of the generalized inverse of a rectangular matrix; the Fredholm pseudoinverse; and perturbations and approximations for generalized inverses and linear operator equations. Subsequent chapters deal with various applications of generalized inverses, including programming, games, and networks, as well as estimation and aggregation in econometrics. This monograph will be of interest to mathematicians and students of mathematics.
Author: David L. Colton
Publisher: SIAM
ISBN: 9780898712520
Category : Mathematics
Languages : en
Pages : 234
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Book Description
Author: Peng Shi
Publisher: Springer Nature
ISBN: 3031009789
Category : Technology & Engineering
Languages : en
Pages : 551
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Book Description
This book, dedicated to Professor Georgi M. Dimirovski on his anniversary, contains new research directions, challenges, and many relevant applications related to many aspects within the broadly perceived areas of systems and control, including signal analysis and intelligent systems. The project comprises two volumes with papers written by well known and very active researchers and practitioners. The first volume is focused on more foundational aspects related to general issues in systems science and mathematical systems, various problems in control and automation, and the use of computational and artificial intelligence in the context of systems modeling and control. The second volume is concerned with a presentation of relevant applications, notably in robotics, computer networks, telecommunication, fault detection/diagnosis, as well as in biology and medicine, and economic, financial, and social systems too.
Author: Miloslav Feistauer
Publisher: Springer Science & Business Media
ISBN: 3642187757
Category : Mathematics
Languages : en
Pages : 873
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Book Description
These proceedings collect the major part of the lectures given at ENU MATH2003, the European Conference on Numerical Mathematics and Ad vanced Applications, held in Prague, Czech Republic, from 18 August to 22 August, 2003. The importance of numerical and computational mathematics and sci entific computing is permanently growing. There is an increasing number of different research areas, where numerical simulation is necessary. Let us men tion fluid dynamics, continuum mechanics, electromagnetism, phase transi tion, cosmology, medicine, economics, finance, etc. The success of applications of numerical methods is conditioned by changing its basic instruments and looking for new appropriate techniques adapted to new problems as well as new computer architectures. The ENUMATH conferences were established in order to provide a fo rum for discussion of current topics of numerical mathematics. They seek to convene leading experts and young scientists with special emphasis on con tributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms as well as in their applications to challenging scientific and industrial problems. The first ENUMATH conference was organized in Paris in 1995, then the series continued by the conferences in Heidelberg 1997, Jyvaskyla 1999 and Ischia Porto 2001. It was a great pleasure and honour for the Czech numerical community that it was decided at Ischia Porto to organize the ENUMATH2003 in Prague. It was the first time when this conference crossed the former Iron Courtain and was organized in a postsocialist country.
Author: Sergey I. Kabanikhin
Publisher: Walter de Gruyter
ISBN: 3110224011
Category : Mathematics
Languages : en
Pages : 476
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Book Description
The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attention of serious researchers. Despite Hadamard's pessimistic forecasts, however, his unloved "child" has turned into a powerful theory whose results are used in many fields of pure and applied mathematics. What is the secret of its success? The answer is clear. Ill-posed problems occur everywhere and it is unreasonable to ignore them. Unlike ill-posed problems, inverse problems have no strict mathematical definition. In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed. The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of ill-posed problems. Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other. Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose a classification of inverse problems according to the type of equation, unknowns and additional information. We consider specific problems from a single position and indicate relationships between them. The problems relate to different areas of mathematics, such as linear algebra, theory of integral equations, integral geometry, spectral theory and mathematical physics. We give examples of applied problems that can be studied using the techniques we describe. This book was conceived as a textbook on the foundations of the theory of inverse and ill-posed problems for university students. The author's intention was to explain this complex material in the most accessible way possible. The monograph is aimed primarily at those who are just beginning to get to grips with inverse and ill-posed problems but we hope that it will be useful to anyone who is interested in the subject.
Author: Nitta, Tohru
Publisher: IGI Global
ISBN: 1605662151
Category : Computers
Languages : en
Pages : 504
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Book Description
"This book covers the current state-of-the-art theories and applications of neural networks with high-dimensional parameters"--Provided by publisher.
