Ill Posed Variational Problems And Regularization Techniques
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| Author | : Michel Thera |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 281 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 3642457800 |
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 approximation, penalization and regularization, - Bundle methods, nonsmooth optimization and regularization, - Error Bounds for regularized optimization problems.
| Author | : Anatoly B. Bakushinsky |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 447 |
| Release | : 2018-02-05 |
| Genre | : Mathematics |
| ISBN | : 3110556383 |
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
| Author | : Curtis R. Vogel |
| Publisher | : SIAM |
| Total Pages | : 195 |
| Release | : 2002-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898717574 |
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
| Author | : Anatoly B. Bakushinsky |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 342 |
| Release | : 2018-02-05 |
| Genre | : Mathematics |
| ISBN | : 3110557355 |
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
| Author | : Peter W. Hawkes |
| Publisher | : Elsevier |
| Total Pages | : 565 |
| Release | : 2003-12-02 |
| Genre | : Technology & Engineering |
| ISBN | : 0080493254 |
The subjects reviewed in the 'Advances' series cover a broad range of themes including microscopy, electromagnetic fields and image coding. Volume 128 concentrates on regularization, a vital aspect of restoration on low voltage scanning electron microscopy.This Book looks at theory and it's application in a practical sense, with a full account of the methods used and realistic detailed application. The authors do this by examining the latest developments, historic illustrations and mathematical fundamentals of the exciting developments in imaging and applying them to realistic practical situationsThe text bridges the gap between academic researchers and R&D designers by addressing and solving daily issues, which makes this book essential reading.·Emphasizes broad and in depth article collaborations between world-renowned scientists in the field of image and electron physics·Presents theory and it's application in a practical sense, providing long awaited solutions and new findings·Bridges the gap between academic researchers and practitioners in industry
| Author | : Vitalii P. Tanana |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 138 |
| Release | : 2018-03-19 |
| Genre | : Mathematics |
| ISBN | : 3110577216 |
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 | : Otmar Scherzer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1626 |
| Release | : 2010-11-23 |
| Genre | : Mathematics |
| ISBN | : 0387929193 |
The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
| Author | : Hedy Attouch |
| Publisher | : SIAM |
| Total Pages | : 794 |
| Release | : 2014-10-02 |
| Genre | : Mathematics |
| ISBN | : 1611973473 |
This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision. This second edition covers several new topics: new section on capacity theory and elements of potential theory now includes the concepts of quasi-open sets and quasi-continuity; increased number of examples in the areas of linearized elasticity system, obstacles problems, convection-diffusion, and semilinear equations; new section on mass transportation problems and the Kantorovich relaxed formulation of the Monge problem; new subsection on stochastic homogenization establishes the mathematical tools coming from ergodic theory; and an entirely new and comprehensive chapter (17) devoted to gradient flows and the dynamical approach to equilibria. The book is intended for Ph.D. students, researchers, and practitioners who want to approach the field of variational analysis in a systematic way.
| Author | : Martin A. Fischler |
| Publisher | : Elsevier |
| Total Pages | : 815 |
| Release | : 2014-06-28 |
| Genre | : Computers |
| ISBN | : 0080515819 |
The field of computer vision combines techniques from physics, mathematics, psychology, artificial intelligence, and computer science to examine how machines might construct meaningful descriptions of their surrounding environment. The editors of this volume, prominent researchers and leaders of the SRI International AI Center Perception Group, have selected sixty papers, most published since 1980, with the viewpoint that computer vision is concerned with solving seven basic problems: - Reconstructing 3D scenes from 2D images - Decomposing images into their component parts - Recognizing and assigning labels to scene objects - Deducing and describing relations among scene objects - Determining the nature of computer architectures that can support the visual function - Representing abstractions in the world of computer memory - Matching stored descriptions to image representation Each chapter of this volume addresses one of these problems through an introductory discussion, which identifies major ideas and summarizes approaches, and through reprints of key research papers. Two appendices on crucial assumptions in image interpretation and on parallel architectures for vision applications, a glossary of technical terms, and a comprehensive bibliography and index complete the volume.
| Author | : Van Hien Nguyen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 512 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 3642570143 |
The 9th Belgian-French-German Conference on Optimization has been held in Namur (Belgium) on September 7-11, 1998. This volume is a collection of papers presented at this Conference. Originally, this Conference was a French-German Conference but this year, in accordance with the organizers' wishes, a third country, Belgium, has joined the founding members of the Conference. Hence the name: Belgian French-German Conference on Optimization. Since the very beginning, the purpose of these Conferences has been to bring together researchers working in the area of Optimization and partic ularly to encourage young researchers to present their work. Most of the participants come from the organizing countries. However the general ten dancy is to invite outside researchers to attend the meeting. So this year, among the 101 participants at this Conference, twenty researchers came from other countries. The general theme of the Conference is everything that concerns the area of Optimization without specification of particular topics. So theoretical as pects of Optimization, in addition to applications and algorithms of Opti mization, will be developed. However, and this point was very important for the organizers, the Conference must retain its convivial character. No more than two parallel sessions are organized. This would allow useful contacts between researchers to be promoted. The editors express their sincere thanks to all those who took part in this Conference. Their invaluable discussions have made this volume possible.
