Methods for Solving Incorrectly Posed Problems

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Publisher : Springer Science & Business Media
ISBN 13 : 1461252806
Total Pages : 275 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Methods for Solving Incorrectly Posed Problems by : V.A. Morozov

Download or read book Methods for Solving Incorrectly Posed Problems written by V.A. Morozov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f € F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D , in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides with A F ("sol vabi li ty" condition); (2) The equality AU = AU for any u ,u € DA implies the I 2 l 2 equality u = u ("uniqueness" condition); l 2 (3) The inverse operator A-I is continuous on F ("stability" condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any "ill-posed" (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation.

Methods for Solving Incorrectly Posed Problems

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Publisher :
ISBN 13 :
Total Pages : 284 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Methods for Solving Incorrectly Posed Problems by : Vladimir Alekseevich Morozov

Download or read book Methods for Solving Incorrectly Posed Problems written by Vladimir Alekseevich Morozov and published by . This book was released on 1984 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Surveys on Solution Methods for Inverse Problems

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Publisher : Springer Science & Business Media
ISBN 13 : 3709162963
Total Pages : 279 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Surveys on Solution Methods for Inverse Problems by : David Colton

Download or read book Surveys on Solution Methods for Inverse Problems written by David Colton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods". This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.

Encyclopaedia of Mathematics

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Publisher : Springer Science & Business Media
ISBN 13 : 9781556080036
Total Pages : 540 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1988 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.

Iterative Methods for Ill-Posed Problems

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Publisher : Walter de Gruyter
ISBN 13 : 3110250659
Total Pages : 153 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Iterative Methods for Ill-Posed Problems by : Anatoly B. Bakushinsky

Download or read book Iterative Methods for Ill-Posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter. This book was released on 2010-12-23 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Methods for Solving Inverse Problems of Mathematical Physics

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Publisher : Walter de Gruyter
ISBN 13 : 3110205793
Total Pages : 453 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Numerical Methods for Solving Inverse Problems of Mathematical Physics by : A. A. Samarskii

Download or read book Numerical Methods for Solving Inverse Problems of Mathematical Physics written by A. A. Samarskii and published by Walter de Gruyter. This book was released on 2008-08-27 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

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Publisher : Walter de Gruyter
ISBN 13 : 3110195305
Total Pages : 245 pages
Book Rating : 4.1/5 (11 download)

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Book Synopsis Well-posed, Ill-posed, and Intermediate Problems with Applications by : Petrov Yuri P.

Download or read book Well-posed, Ill-posed, and Intermediate Problems with Applications written by Petrov Yuri P. and published by Walter de Gruyter. This book was released on 2011-12-22 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Optimal Methods for Ill-Posed Problems

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110577216
Total Pages : 138 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Optimal Methods for Ill-Posed Problems by : Vitalii P. Tanana

Download or read book Optimal Methods for Ill-Posed Problems written by Vitalii P. Tanana and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-03-19 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Ill-Posed Problems in Natural Sciences

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112313933
Total Pages : 608 pages
Book Rating : 4.1/5 (123 download)

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Book Synopsis Ill-Posed Problems in Natural Sciences by : Andrei N. Tikhonov

Download or read book Ill-Posed Problems in Natural Sciences written by Andrei N. Tikhonov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Ill-Posed Problems in Natural Sciences".

Non-Standard and Improperly Posed Problems

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Publisher : Elsevier
ISBN 13 : 008053774X
Total Pages : 319 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Non-Standard and Improperly Posed Problems by : William F. Ames

Download or read book Non-Standard and Improperly Posed Problems written by William F. Ames and published by Elsevier. This book was released on 1997-07-07 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions on the initial conditions and the modeling equations--and on problems for which data are only prescribed on part of the boundary. The book addresses continuous dependence on initial-time and spatial geometry and on modeling backward and forward in time. It covers non-standard or non-characteristic problems, such as the sideways problem for a heat or hyberbolic equation and the Cauchy problem for the Laplace equation and other elliptic equations. The text also presents other relevant improperly posed problems, including the uniqueness and continuous dependence for singular equations, the spatial decay in improperly posed parabolicproblems, the uniqueness for the backward in time Navier-Stokes equations on an unbounded domain, the improperly posed problems for dusty gases, the linear thermoelasticity, and the overcoming Holder continuity and image restoration. Provides the first unified survey of the advances made in the last 15 years in the field Includes an up-to-date compendium of the mathematical literature on these topics

Regularization Methods for Ill-posed Problems

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Publisher : CRC PressI Llc
ISBN 13 : 9780849393112
Total Pages : 257 pages
Book Rating : 4.3/5 (931 download)

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Book Synopsis Regularization Methods for Ill-posed Problems by : Vladimir Alekseevich Morozov

Download or read book Regularization Methods for Ill-posed Problems written by Vladimir Alekseevich Morozov and published by CRC PressI Llc. This book was released on 1993 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents current theories and methods for obtaining approximate solutions of basic classes of incorrectly posed problems. The book provides simple conditions of optimality and the optimality of the order of regular methods for solving a wide class of unsteady problems.

Upper Main Sequence Stars with Anomalous Abundances

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Publisher : Springer Science & Business Media
ISBN 13 : 9400947143
Total Pages : 476 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Upper Main Sequence Stars with Anomalous Abundances by : C.R. Cowley

Download or read book Upper Main Sequence Stars with Anomalous Abundances written by C.R. Cowley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers presented at IAU Colloquium No. 90. at the Crimean Astrophysical Observatory in May of 1985. A few additional contributions are included from authors who for various reasons were unable to attend the meeting. Four years have passed since the last major international conference on chemically peculiar stars of the upper main sequence was held in Liege. Belgium in 1981. Previous conferences were held in 1975 (Vienna. Austria) and in 1965 (Greenbelt. Maryland. USA). As the proceedings of this Colloquium show. the recent availability of ultraviolet spectra of large numbers of normal and chemically peculiar A and B stars is having a major impact on the way we study these objects. and has led to many new. exciting and unanticipated results. Simultaneously. the more traditional study of optical spectra has been advanced through the increasing use of very high spectral resolution with high signal-to-noise detectors. The chemically peculiar (CP) stars on the upper main sequence belong in the standard framework within which we understand stellar evolution and the history of matter. Recent work has made it clear that the unusual chemistry and magnetic structure of these objects is of relevance across the broad domain of stellar astronomy. from the upper main sequence to horizontal branch stars and white dwarfs. Metal poor (J>. Boo) as well as metal rich (Ap. Am) stars are an integral part of the picture.

Fast Solution of Discretized Optimization Problems

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Publisher : Birkhäuser
ISBN 13 : 3034882335
Total Pages : 292 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Fast Solution of Discretized Optimization Problems by : Karl-Heinz Hoffmann

Download or read book Fast Solution of Discretized Optimization Problems written by Karl-Heinz Hoffmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.

Numerical Methods for the Solution of Ill-Posed Problems

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Publisher : Springer Science & Business Media
ISBN 13 : 940158480X
Total Pages : 257 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Numerical Methods for the Solution of Ill-Posed Problems by : A.N. Tikhonov

Download or read book Numerical Methods for the Solution of Ill-Posed Problems written by A.N. Tikhonov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Analytic Computational Methods in Applied Mathematics

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Publisher : CRC Press
ISBN 13 : 0429525117
Total Pages : 413 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis Handbook of Analytic Computational Methods in Applied Mathematics by : George Anastassiou

Download or read book Handbook of Analytic Computational Methods in Applied Mathematics written by George Anastassiou and published by CRC Press. This book was released on 2019-06-03 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f

Proceedings of the 4th International Conference on Communication, Devices and Computing

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Publisher : Springer Nature
ISBN 13 : 9819927102
Total Pages : 698 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Proceedings of the 4th International Conference on Communication, Devices and Computing by : Dilip Kumar Sarkar

Download or read book Proceedings of the 4th International Conference on Communication, Devices and Computing written by Dilip Kumar Sarkar and published by Springer Nature. This book was released on 2023-08-28 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of best selected research papers presented at the Fourth International Conference on Communication, Devices and Computing (ICCDC 2023). The book covers new ideas, applications and experiences of research engineers, scientists, industrialists, scholars and students from in and around the globe. It covers research contributions from communication technologies which are from the areas such as 5G communication, next-generation Wi-Fi, spread spectrum systems, satellite and high altitude platforms, radio over fiber techniques, wireless sensor networks, modulation and diversity technique, ad hoc and mesh networks, cognitive radio networking, optical wireless and visible light communications, signal processing for secure communication, millimeter wave and terahertz communication, design, control and management of optical network, error control coding and information theory, printed antennas, performance analysis of wireless network, smart antennas and space time processing.

Perspectives in Mathematical Sciences

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Publisher : World Scientific
ISBN 13 : 9814289302
Total Pages : 371 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Perspectives in Mathematical Sciences by : Yisong Yang

Download or read book Perspectives in Mathematical Sciences written by Yisong Yang and published by World Scientific. This book was released on 2010 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gun Shy