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Regularization Algorithms for Ill-Posed Problems, Bakushinsky Anatoly B., Kokurin Mikhail M., Kokurin Mikhail Yu


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Автор: Bakushinsky Anatoly B., Kokurin Mikhail M., Kokurin Mikhail Yu
Название:  Regularization Algorithms for Ill-Posed Problems
ISBN: 9783110556308
Издательство: Walter de Gruyter
Издательство: de Gruyter
Классификация:




ISBN-10: 3110556308
Обложка/Формат: Hardcover
Страницы: 342
Вес: 0.68 кг.
Дата издания: 05.02.2018
Язык: English
Размер: 24.38 x 17.27 x 2.29 cm
Поставляется из: США
Описание:

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




Regularization of Ill-Posed Problems by Iteration Methods

Автор: S.F. Gilyazov; N.L. Gol`dman
Название: Regularization of Ill-Posed Problems by Iteration Methods
ISBN: 9048153824 ISBN-13(EAN): 9789048153824
Издательство: Springer
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Цена: 13974.00 р.
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Описание: Iteration regularization, i.e., utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems.

Ill-posed Variational Problems and Regularization Techniques

Автор: Michel Thera; Rainer Tichatschke
Название: Ill-posed Variational Problems and Regularization Techniques
ISBN: 3540663231 ISBN-13(EAN): 9783540663232
Издательство: Springer
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Цена: 15372.00 р.
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Описание: Developments in the field of ill-posed variational problems and variational inequalities are presented here. The work covers a large range of theoretical, numerical and practical aspects.

Regularization of Ill-Posed Problems by Iteration Methods

Автор: S.F. Gilyazov; N.L. Gol`dman
Название: Regularization of Ill-Posed Problems by Iteration Methods
ISBN: 0792361318 ISBN-13(EAN): 9780792361312
Издательство: Springer
Рейтинг:
Цена: 15372.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: Iteration regularization, i.e., utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems.

Optimization Techniques in Computer Vision

Автор: Mongi A. Abidi; Andrei V. Gribok; Joonki Paik
Название: Optimization Techniques in Computer Vision
ISBN: 3319463632 ISBN-13(EAN): 9783319463636
Издательство: Springer
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Цена: 18167.00 р.
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Описание: This book presents practical optimization techniques used in image processing and computer vision problems. Ill-posed problems are introduced and used as examples to show how each type of problem is related to typical image processing and computer vision problems. Unconstrained optimization gives the best solution based on numerical minimization of a single, scalar-valued objective function or cost function. Unconstrained optimization problems have been intensively studied, and many algorithms and tools have been developed to solve them. Most practical optimization problems, however, arise with a set of constraints. Typical examples of constraints include: (i) pre-specified pixel intensity range, (ii) smoothness or correlation with neighboring information, (iii) existence on a certain contour of lines or curves, and (iv) given statistical or spectral characteristics of the solution. Regularized optimization is a special method used to solve a class of constrained optimization problems. The term regularization refers to the transformation of an objective function with constraints into a different objective function, automatically reflecting constraints in the unconstrained minimization process. Because of its simplicity and efficiency, regularized optimization has many application areas, such as image restoration, image reconstruction, optical flow estimation, etc.

Optimization plays a major role in a wide variety of theories for image processing and computer vision. Various optimization techniques are used at different levels for these problems, and this volume summarizes and explains these techniques as applied to image processing and computer vision.
Numerical Regularization for Atmospheric Inverse Problems

Автор: Adrian Doicu; Thomas Trautmann; Franz Schreier
Название: Numerical Regularization for Atmospheric Inverse Problems
ISBN: 3642424015 ISBN-13(EAN): 9783642424014
Издательство: Springer
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Цена: 26120.00 р.
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Описание: Written by brilliant mathematicians, this research monograph presents and analyzes numerical algorithms for atmospheric retrieval, pulling together all the relevant material in a consistent, very powerful manner.

Regularization of Inverse Problems

Автор: Heinz Werner Engl; Martin Hanke; A. Neubauer
Название: Regularization of Inverse Problems
ISBN: 0792341570 ISBN-13(EAN): 9780792341574
Издательство: Springer
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Цена: 15372.00 р.
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Описание: Offers an overview over some classes of inverse problems. This book deals with the mathematical theory of regularization methods and gives an account of the results about regularization methods both for linear and for nonlinear ill-posed problems. It considers both continuous and iterative regularization methods.

Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization

Автор: Flemming
Название: Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization
ISBN: 3319952633 ISBN-13(EAN): 9783319952635
Издательство: Springer
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Цена: 7685.00 р.
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Описание: The book collects and contributes new results on the theory and practice of ill-posed inverse problems. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view.

Variational Regularization for Systems of Inverse Problems

Автор: Richard Huber
Название: Variational Regularization for Systems of Inverse Problems
ISBN: 3658253894 ISBN-13(EAN): 9783658253899
Издательство: Springer
Рейтинг:
Цена: 7685.00 р.
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Описание: Tikhonov regularization is a cornerstone technique in solving inverse problems with applications in countless scienti?c ?elds. Richard Huber discusses a multi-parameter Tikhonov approach for systems of inverse problems in order to take advantage of their speci?c structure. Such an approach allows to choose the regularization weights of each subproblem individually with respect to the corresponding noise levels and degrees of ill-posedness.

Optimization and Regularization for Computational Inverse Problems and Applications

Автор: Wang Yanfei, Yagola Anatoly G., Yang Changchun
Название: Optimization and Regularization for Computational Inverse Problems and Applications
ISBN: 3642137415 ISBN-13(EAN): 9783642137419
Издательство: Springer
Рейтинг:
Цена: 13974.00 р.
Наличие на складе: Нет в наличии.

Описание: This book covers both the methods, including standard regularization theory, Fejer processes for linear and nonlinear problems, the balancing principle, extrapolated regularization, nonstandard regularization, nonlinear gradient method, the nonmonotone gradient method, subspace method and Lie group method;

The Kepler Problem

Автор: Bruno Cordani
Название: The Kepler Problem
ISBN: 303489421X ISBN-13(EAN): 9783034894210
Издательство: Springer
Рейтинг:
Цена: 13974.00 р.
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Описание: Because of the correspondences existing among all levels of reality, truths pertaining to a lower level can be considered as symbols of truths at a higher level and can therefore be the "foundation" or support leading by analogy to a knowledge of the latter.

Regularization in Orbital Mechanics: Theory and Practice

Автор: Javier Roa
Название: Regularization in Orbital Mechanics: Theory and Practice
ISBN: 3110558556 ISBN-13(EAN): 9783110558555
Издательство: Walter de Gruyter
Цена: 21013.00 р.
Наличие на складе: Есть у поставщика Поставка под заказ.

Описание:

Regularized equations of motion can improve numerical integration for the propagation of orbits, and simplify the treatment of mission design problems. This monograph discusses standard techniques and recent research in the area. While each scheme is derived analytically, its accuracy is investigated numerically. Algebraic and topological aspects of the formulations are studied, as well as their application to practical scenarios such as spacecraft relative motion and new low-thrust trajectories.

Stochastic Calculus via Regularizations

Автор: Russo
Название: Stochastic Calculus via Regularizations
ISBN: 303109445X ISBN-13(EAN): 9783031094453
Издательство: Springer
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Цена: 22359.00 р.
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Описание: The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the other hand it focuses on the techniques of stochastic integration and calculus via regularization initiated by the authors. The definitions relies on a smoothing procedure of the integrator process, they generalize the usual It? and Stratonovich integrals for Brownian motion but the integrator could also not be a semimartingale and the integrand is allowed to be anticipating. The resulting calculus requires a simple formalism: nevertheless it entails pathwise techniques even though it takes into account randomness. It allows connecting different types of pathwise and non pathwise integrals such as Young, fractional, Skorohod integrals, enlargement of filtration and rough paths. The covariation, but also high order variations, play a fundamental role in the calculus via regularization, which can also be applied for irregular integrators. A large class of Gaussian processes, various generalizations of semimartingales such that Dirichlet and weak Dirichlet processes are revisited. Stochastic calculus via regularization has been successfully used in applications, for instance in robust finance and on modeling vortex filaments in turbulence. The book is addressed to PhD students and researchers in stochastic analysis and applications to various fields.


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