Optimal Methods For Ill Posed Problems

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Optimal Methods For Ill Posed Problems

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Author : Vitalii P. Tanana
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-03-19

Optimal Methods For Ill Posed Problems written by Vitalii P. Tanana and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.

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

Inverse And Ill Posed Problems

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Author : Heinz W. Engl
language : en
Publisher:
Release Date : 1987

Inverse And Ill Posed Problems written by Heinz W. Engl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Inverse and Ill-Posed Problems.

Computational Methods For Inverse Problems

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Author : Curtis R. Vogel
language : en
Publisher: SIAM
Release Date : 2002-01-01

Computational Methods For Inverse Problems written by Curtis R. Vogel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.

Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Numerical Methods For The Solution Of Ill Posed Problems

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Author : A.N. Tikhonov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Numerical Methods For The Solution Of Ill Posed Problems written by A.N. Tikhonov 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 2013-03-09 with Mathematics categories.

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.

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.

Regularization Algorithms For Ill Posed Problems

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Author : Anatoly B. Bakushinsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05

Regularization Algorithms For Ill Posed Problems written by Anatoly B. Bakushinsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.

This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems

Ill Posed Problems In Optimal Control Systems And A Method To Solve Them

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Author : Lili Hedayatolah-Tabrizi
language : en
Publisher:
Release Date : 1983

Ill Posed Problems In Optimal Control Systems And A Method To Solve Them written by Lili Hedayatolah-Tabrizi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Control theory categories.

Optimal Methods For Ill Posed Problems

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Author : Vitalii P. Tanana
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-03-19

Optimal Methods For Ill Posed Problems written by Vitalii P. Tanana and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.

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

Nonlinear Ill Posed Problems

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Author : A.N. Tikhonov
language : en
Publisher: Springer
Release Date : 2014-08-23

Nonlinear Ill Posed Problems written by A.N. Tikhonov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-23 with Mathematics categories.

Multidisciplinary Methods For Analysis Optimization And Control Of Complex Systems

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Author : Vincenzo Capasso
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-05

Multidisciplinary Methods For Analysis Optimization And Control Of Complex Systems written by Vincenzo Capasso 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 2006-01-05 with Mathematics categories.

This book consists of lecture notes of a summer school named after the late Jacques Louis Lions. The summer school was designed to alert both Academia and Industry to the increasing role of multidisciplinary methods and tools for the design of complex products in various areas of socio-economic interest. This volume offers the reader a rare opportunity of being exposed to the presentation of real industrial and societal problems together with the relevant innovative methods used.