Well Posed Ill Posed And Intermediate Problems With Applications
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Well Posed Ill Posed And Intermediate Problems With Applications
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Author : Petrov Yuri P.
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Well Posed Ill Posed And Intermediate Problems With Applications written by Petrov Yuri P. and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.
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.
Operator Theory And Ill Posed Problems
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Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Operator Theory And Ill Posed Problems written by Mikhail M. Lavrent'ev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.
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.
Computer Algebra In Scientific Computing
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Author : François Boulier
language : en
Publisher: Springer Nature
Release Date : 2021-08-16
Computer Algebra In Scientific Computing written by François Boulier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-16 with Computers categories.
This book constitutes the proceedings of the 23rd International Workshop on Computer Algebra in Scientific Computing, CASC 2021, held in Sochi, Russia, in September 2021. The 24 full papers presented together with 1 invited talk were carefully reviewed and selected from 40 submissions. The papers cover theoretical computer algebra and its applications in scientific computing.
Numerical Mathematics And Advanced Applications
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Author : Miloslav Feistauer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Mathematics And Advanced Applications written by Miloslav Feistauer 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.
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.
Continuum Theory And Modeling Of Thermoelectric Elements
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Author : Christophe Goupil
language : en
Publisher: John Wiley & Sons
Release Date : 2016-02-23
Continuum Theory And Modeling Of Thermoelectric Elements written by Christophe Goupil and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-23 with Science categories.
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.
Inverse Problems In Partial Differential Equations
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Author : David L. Colton
language : en
Publisher: SIAM
Release Date : 1990-01-01
Inverse Problems In Partial Differential Equations written by David L. Colton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
Inverse Problems In Diffusion Processes
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Author : Heinz W. Engl
language : en
Publisher: SIAM
Release Date : 1995-01-01
Inverse Problems In Diffusion Processes written by Heinz W. Engl and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.
This collection of expository papers encompasses both the theoretical and physical application side of inverse problems in diffusion processes.
Inverse Problems With Applications In Science And Engineering
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Author : Daniel Lesnic
language : en
Publisher: CRC Press
Release Date : 2021-11-09
Inverse Problems With Applications In Science And Engineering written by Daniel Lesnic and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-09 with Mathematics categories.
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
Conjugate Gradient Type Methods For Ill Posed Problems
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Author : Martin Hanke
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Conjugate Gradient Type Methods For Ill Posed Problems written by Martin Hanke and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.
Complex Systems Spanning Control And Computational Cybernetics Applications
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Author : Peng Shi
language : en
Publisher: Springer Nature
Release Date : 2022-09-18
Complex Systems Spanning Control And Computational Cybernetics Applications written by Peng Shi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-18 with Technology & Engineering categories.
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.