Methods For Solving Incorrectly Posed Problems

Author : V.A. Morozov
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461252801

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Methods for Solving Incorrectly Posed Problems by V.A. Morozov Pdf

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.

Author : Vladimir Alekseevich Morozov
Publisher : Unknown
Page : 284 pages
File Size : 55,8 Mb
Release : 1984
Category : Differential equations, Partial
ISBN : UCAL:B4405509

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Methods for Solving Incorrectly Posed Problems by Vladimir Alekseevich Morozov Pdf

Author : David Colton,Heinz W. Engl,Alfred K. Louis,Joyce McLaughlin,William Rundell
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783709162965

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Surveys on Solution Methods for Inverse Problems by David Colton,Heinz W. Engl,Alfred K. Louis,Joyce McLaughlin,William Rundell Pdf

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.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 54,5 Mb
Release : 1988
Category : Mathematics
ISBN : 1556080034

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

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.

Author : Andrei N. Tikhonov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 608 pages
File Size : 54,7 Mb
Release : 2020-05-18
Category : Mathematics
ISBN : 9783112313930

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Ill-Posed Problems in Natural Sciences by Andrei N. Tikhonov Pdf

No detailed description available for "Ill-Posed Problems in Natural Sciences".

Author : Vitalii P. Tanana,Anna I. Sidikova
Publisher : Walter de Gruyter GmbH & Co KG
Page : 138 pages
File Size : 42,5 Mb
Release : 2018-03-19
Category : Mathematics
ISBN : 9783110577211

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Optimal Methods for Ill-Posed Problems by Vitalii P. Tanana,Anna I. Sidikova Pdf

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

Author : C.R. Cowley,M.M. Dworetsky,C. Mégessier
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400947146

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Upper Main Sequence Stars with Anomalous Abundances by C.R. Cowley,M.M. Dworetsky,C. Mégessier Pdf

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.

Author : Karl-Heinz Hoffmann,Ronald W. Hoppe,Volker Schulz
Publisher : Birkhäuser
Page : 292 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882330

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Fast Solution of Discretized Optimization Problems by Karl-Heinz Hoffmann,Ronald W. Hoppe,Volker Schulz Pdf

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.

Author : George Anastassiou
Publisher : CRC Press
Page : 413 pages
File Size : 41,5 Mb
Release : 2019-06-03
Category : Mathematics
ISBN : 9780429525117

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Handbook of Analytic Computational Methods in Applied Mathematics by George Anastassiou Pdf

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

Author : Dilip Kumar Sarkar,Pradip Kumar Sadhu,Sunandan Bhunia,Jagannath Samanta,Suman Paul
Publisher : Springer Nature
Page : 698 pages
File Size : 50,7 Mb
Release : 2023-08-28
Category : Technology & Engineering
ISBN : 9789819927104

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Proceedings of the 4th International Conference on Communication, Devices and Computing by Dilip Kumar Sarkar,Pradip Kumar Sadhu,Sunandan Bhunia,Jagannath Samanta,Suman Paul Pdf

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.

Author : Yisong Yang,Jinqiao Duan,Xinchu Fu
Publisher : World Scientific
Page : 371 pages
File Size : 44,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814289313

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Perspectives in Mathematical Sciences by Yisong Yang,Jinqiao Duan,Xinchu Fu Pdf

1. Periodic boundary problems for analytic function including automorphic functions / Haitao Cai and Jian-Ke Lu -- 2. Subharmonic bifurcations and chaos for a model of micro-cantilever in MEMS / Yushu Chen, Liangqiang Zhou and Fangqi Chen -- 3. Canonical sample spaces for random dynamical systems / Jinqiao Duan, Xingye Kan and Bjorn Schmalfuss -- 4. Epidemic propagation dynamics on complex networks / Xinchu Fu ... [et al.] -- 5. Inverse problems for equations of parabolic type / Zhibin Han, Yongzhong Huang and Ming Jian -- 6. The existence and asymptotic properties of nontrivial solutions of nonlinear (2 - q)-Laplacian type problems with linking geometric structure / Gongbao Li and Zhaofen Shen -- 7. Chaotic dynamics for the two-component Bose-Einstein condensate system / Jibin Li -- 8. Recent developments and perspectives in nonlinear dynamics / Zengrong Liu -- 9. Mathematical aspects of the cold plasma model / Thomas H. Otway -- 10. Gravitating Yang-Mills fields in all dimensions / Eugen Radu and D. H. Tchrakian -- 11. Hamiltonian constraint and Mandelstam identities over extended knot families [symbol] and [symbol] in extended loop gravity / Dan Shao, Liang Shao and Changgui Shao -- 12. Lattice Boltzmann simulation of nonlinear Schrödinger equation with variable coefficients / Baochang Shi -- 13. Exponential stability of nonlocal time-delayed burgers equation / Yanbin Tang -- 14. Bifurcation analysis of the Swift-Hohenberg equation with quintic nonlinearity and Neumann boundary condition / Qingkun Xiao and Hongjun Gao -- 15. A new GL method for mathematical and physical problems / Ganquan Xie and Jianhua Li -- 16. Harmonically representing topological classes / Yisong Yang.

Author : Vladimir Alekseevich Morozov
Publisher : CRC PressI Llc
Page : 257 pages
File Size : 50,6 Mb
Release : 1993
Category : Mathematics
ISBN : 0849393116

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Regularization Methods for Ill-posed Problems by Vladimir Alekseevich Morozov Pdf

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.

Author : James P. Hartnett
Publisher : Elsevier
Page : 302 pages
File Size : 48,6 Mb
Release : 2002-07-25
Category : Technology & Engineering
ISBN : 9780080526751

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Advances in Heat Transfer by James P. Hartnett Pdf

Advances in Heat Transfer

Author : Charles W. Groetsch
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 50,8 Mb
Release : 2013-12-14
Category : Technology & Engineering
ISBN : 9783322992024

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Inverse Problems in the Mathematical Sciences by Charles W. Groetsch Pdf

Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book are: causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.

Author : Heinz W. Engl,Alfred K. Louis,William Rundell
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Medical
ISBN : 9783709165218

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Inverse Problems in Medical Imaging and Nondestructive Testing by Heinz W. Engl,Alfred K. Louis,William Rundell Pdf

14 contributions present mathematical models for different imaging techniques in medicine and nondestructive testing. The underlying mathematical models are presented in a way that also newcomers in the field have a chance to understand the relation between the special applications and the mathematics needed for successfully treating these problems. The reader gets an insight into a modern field of scientific computing with applications formerly not presented in such form, leading from the basics to actual research activities.