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Linear Operators and Ill-Posed Problems
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M M Lavrent'ev, L Ya Savel'ev
In this easily-accessible textbook, the authors integrate the ill-posed problem theory and its underlying mathematical apparatus. This comprehensive work includes descriptions of recent results and a presentation of actual applications of the ill-posed problem theory. The first part of the book describes the differentiation of normed space ...
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Well-Posed Optimization Problems
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A L Dontchev
This book presents in a unified way the mathematical theory of well-posedness in optimization. The basic concepts of well-posedness and the links among them are studied, in particular Hadamard and Tykhonov wellposedness. Abstract optimization problems as well as applications to optimal control, calculus of variations and mathematical programming ...
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Non-Standard and Improperly Posed Problems
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Karen A Ames, Brian Straughan, K A Ames Straughan
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 ...
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The Mollification Method and the Numerical Solution of Ill-Posed Problems
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Diego A Murio
Provides a logical introduction to the area of applied inverse theory (ill-posed problems). The mollification method, developed by the author, is described from a mathematical viewpoint.
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Regularization of Ill-Posed Problems by Iteration Methods
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S F Giliazov, Gilyazov
This volume presents new results in regularization of ill-posed problems by iteration methods, which is one of the most important and rapidly developing topics of the theory of ill-posed problems. The new theoretical results are connected with the proposed united approach to the proof of regularizing properties of the 'classical' iteration methods ...
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Ill-Posed Variational Problems and Regularization Techniques
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by
M Thera
This book presents recent developments in the field of ill-posed variational problems and variational inequalities, covering a large range of theoretical, numerical and practical aspects. The main topics are:- Regularization techniques for equilibrium and fixed point problems, variational inequalities and complementary problems, - Links between ...
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Nonlinear Ill-Posed Problems of Monotone Type
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Yakov Alber, Irina Ryazantseva
Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given ...
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Improperly Posed Problems in Partial Differential Equations
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L. E. Payne
Improperly posed Cauchy problems are the primary topics in this discussion which assumes that the geometry and coefficients of the equations are known precisely. Appropriate references are made to other classes of improperly posed problems. The contents include straight forward examples of methods eigenfunction, quasireversibility, logarithmic ...
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Numerical Methods for the Solution of Ill-Posed Problems
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A N Tikonov, A V Goncharsky, V V Stepanov
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 ...
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Ill-Posed Problems: Theory and Applications
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by
A B Bakushinskii, A Goncharsky
This volume presents a unified approach to the solution of ill-posed problems, based on the concept of a regularizing algorithm (RA). This idea is then explored in depth in the discussion of topics such as common conditions for the existence of regularizing algorithms, necessary and sufficient conditions of the approximations for linear problems, ...
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Metastability and Incompletely Posed Problems
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Stuart S Antman (Editor), J L Ericksen (Editor), David Kinderlehrer (Editor)
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Ill-Posed Problems for Integrodifferential Equations in Mechanics and Electromagnetic Theory
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by
Frederick Bloom
Examines ill-posed, initial-history boundary-value problems associated with systems of partial-integrodifferential equations arising in linear and nonlinear theories of mechanical viscoelasticity, rigid nonconducting material dielectrics, and heat conductors with memory. Variants of two differential inequalities, logarithmic convexity, and ...
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Advances in Electronics & Electron Physics
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Peter W Hawkes (Editor)
This series covers topics ranging from the particle optics of accelerators, mass spectrometers, electron- and ion-microscopes, and their components to theoretical and practical aspects of modern electronics. Also covered is digital image processing and pattern recognition, including the devices employed and the methods developed.
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Inverse problems : an interdisciplinary study
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by
Pierre Celestin Sabatier, Centre national de la recherche scientifique (France)
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Ill-Posed Problems of Mathematical Physics and Analysis
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M. M. Lavrent'ev, S. P. Shishatskii, V. G. Romanov
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Inverse and Ill-Posed Problems Series, Theory of Linear Ill-Posed Problems and Its Applications
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by
Valentin Konstantinovich Ivanov, Vitalifi Pavlovich Tanana (Editor), V V Vasin (Editor)
This monograph is a revised version of the Russian-language edition from 1978. Topics include the structure of sets of uniform regularization, the theory of error estimation and the optimality of methods. It also considers ill-posed problems in Banach spaces.
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Ill-Posed Problems with a Priori Information
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by
V V Vasin, A L Ageev
This work deals with economic and flexible regular methods for solving ill-posed (unstable) problems. These methods take into account additional information on the desired solution. The authors have considered the following unstable problems: linear and nonlinear integral equations, the finite-moment problem, mathematical programming problems, ...
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Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems
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by
O M Alifanov
This monograph is based on the author's studies carried out to investigate one of the most promising trends in the theory of ill-posed problems, namely, iterative regularization and its application to inverse heat transfer problems. Effective methods for solving inverse problems have allowed researchers to simplify experiments considerably, and to ...
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Methods for solving incorrectly posed problems
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by
Morozov
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Nonlinear Ill-Posed Problems
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by
A N Tikhonov
This is an introduction to the theory of non-linear ill-posed problems. It considers applications in linear algebra, vibrational spectroscopy, astrophysics and medicine.
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Solutions of Ill-Posed Problems
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by
A N Tikhonov
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Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis: Proceedings of the International Conference, Samarkand, Uzbekistan
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by
S I Kabanikhin (Editor), M M Lavrent'ev
This volume contains invited and selected papers from the "International Conference Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis", held in Samarkand. Uzbekistan, September 2000. The scientific program consisted of the following topics: theory of ill-posed problems; inverse problems for differential equations; boundary ...
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Inverse Stefan Problems
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by
N L Gol'dman
This monograph presents new theory and methods of solving inverse Stefan problems for quasilinear parabolic equations in domains with free boundaries. This new approach to the theory of ill-posed problems is useful for the modelling of nonlinear processes with phase transforms in thermophysics and mechanics of continuous media. Regularization ...
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Nonlinear Ill-Posed Problems
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by
A I Leonov, A N Tikhonov, A G Yagola
Often many scientific, technological and engineering problems turn out to be ill-pose; meaning they have no solution, no unique solution or an unstable solution. Where searching generalized solutions fails to solve the problem, regularizing algorithms of discrepancy, quasisolutions and smoothing functions are used. Professor A N Tikhonov was the ...
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Regularization Methods for Ill-Posed Problems
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by
V A Morozov
"Regularization Methods for Ill-Posed Problems" 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. It also covers the problem of ...
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