Regularization For Applied Inverse And Ill Posed Problems
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Regularization For Applied Inverse And Ill Posed Problems
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Author :
language : de
Publisher: Springer-Verlag
Release Date : 2013-11-22
Regularization For Applied Inverse And Ill Posed Problems written by and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Technology & Engineering categories.
Iterative Methods For Ill Posed Problems
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Author : Anatoly B. Bakushinsky
language : en
Publisher: Walter de Gruyter
Release Date : 2010-12-23
Iterative Methods For Ill Posed Problems written by Anatoly B. Bakushinsky 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 2010-12-23 with Mathematics categories.
Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.
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
Inverse Problems And Spectral Theory
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Author : Hiroshi Isozaki
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Inverse Problems And Spectral Theory written by Hiroshi Isozaki and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This volume grew out of a workshop on spectral theory of differential operators and inverse problems held at the Research Institute for Mathematical Sciences (Kyoto University). The gathering of nearly 100 participants at the conference suggests the increasing interest in this field of research. The focus of the book is on spectral theory for differential operators and related inverse problems. It includes selected topics from the following areas: electromagnetism, elasticity, the Schrodinger equation, differential geometry, and numerical analysis. The material is suitable for graduate students and researchers interested in inverse problems and their applications.
Handbook Of Analytic Computational Methods In Applied Mathematics
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Author : George Anastassiou
language : en
Publisher: CRC Press
Release Date : 2019-06-03
Handbook Of Analytic Computational Methods In Applied Mathematics written by George Anastassiou and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-03 with Mathematics categories.
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
An Introduction To The Mathematical Theory Of Inverse Problems
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Author : Andreas Kirsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-24
An Introduction To The Mathematical Theory Of Inverse Problems written by Andreas Kirsch 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 2011-03-24 with Mathematics categories.
This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces the reader to the inverse problem of electrical impedance tomography.
Regularized Image Reconstruction In Parallel Mri With Matlab
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Author : Joseph Suresh Paul
language : en
Publisher: CRC Press
Release Date : 2019-11-05
Regularized Image Reconstruction In Parallel Mri With Matlab written by Joseph Suresh Paul and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-05 with Medical categories.
Regularization becomes an integral part of the reconstruction process in accelerated parallel magnetic resonance imaging (pMRI) due to the need for utilizing the most discriminative information in the form of parsimonious models to generate high quality images with reduced noise and artifacts. Apart from providing a detailed overview and implementation details of various pMRI reconstruction methods, Regularized image reconstruction in parallel MRI with MATLAB examples interprets regularized image reconstruction in pMRI as a means to effectively control the balance between two specific types of error signals to either improve the accuracy in estimation of missing samples, or speed up the estimation process. The first type corresponds to the modeling error between acquired and their estimated values. The second type arises due to the perturbation of k-space values in autocalibration methods or sparse approximation in the compressed sensing based reconstruction model. Features: Provides details for optimizing regularization parameters in each type of reconstruction. Presents comparison of regularization approaches for each type of pMRI reconstruction. Includes discussion of case studies using clinically acquired data. MATLAB codes are provided for each reconstruction type. Contains method-wise description of adapting regularization to optimize speed and accuracy. This book serves as a reference material for researchers and students involved in development of pMRI reconstruction methods. Industry practitioners concerned with how to apply regularization in pMRI reconstruction will find this book most useful.
Theory And Practice Of Geophysical Data Inversion
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Author : Andreas Vogel
language : en
Publisher: Vieweg+Teubner Verlag
Release Date : 2012-12-06
Theory And Practice Of Geophysical Data Inversion written by Andreas Vogel and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The contributions to this volume cover a wide spectrum of recent developments in geophysical data inversion, including basic mathematics and general theory, numerical methods, as well as computer implementation of algorithms. Most of the papers are motivated by problems arising from geophysical research and applications both on a global scale and with respect to local geophysical surveys, underlining the increasing importance of geophysical exploration methods in various fields, such as structural geology, prospecting for mineral and energy resources, hydro geology, geotechnology, environmental protection and archaeology. The first section of the book deals with basic mathematics and general theory underlying geophysical data inversion. Papers presented here are concerned with stabilization algorithms to solve ill-posed inverse problems, sensitivity of kernel function estimations to random data errors and reduction of errors in inverse modelling of response functions by linear constraints, numerical procedures for approximating the solution to boundary value problems, accuracy and stability of inverse ill-posed problems constituted by problems of moments, and fast Fourier transforms for solving potential field problems. The second section contains papers on gravity and magnetics, dealing with the solvability of the inverse gravimetric problem for sources represented by point masses and other elementary, solution of the inverse problem in cases of nonuniformly distributed data as obtained by palaeomagnetic studies, satellite observations, and surface projections of buried archaeological targets by inverse filtering of geomagnetic data.
Theory And Applications Of Nonlinear Operators Of Accretive And Monotone Type
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Author : Athanass Kartsatos
language : en
Publisher: CRC Press
Release Date : 1996-03-14
Theory And Applications Of Nonlinear Operators Of Accretive And Monotone Type written by Athanass Kartsatos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-14 with Mathematics categories.
This work is based upon a Special Session on the Theory and Applications of Nonlinear Operators of Accretive and Monotone Type held during the recent meeting of the American Mathematical Society in San Francisco. It examines current developments in non-linear analysis, emphasizing accretive and monotone operator theory. The book presents a major survey/research article on partial functional differential equations with delay and an important survey/research article on approximation solvability.
Applied Inverse Problems
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Author : Larisa Beilina
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-15
Applied Inverse Problems written by Larisa Beilina 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 2013-08-15 with Science categories.
This proceedings volume is based on papers presented at the First Annual Workshop on Inverse Problems which was held in June 2011 at the Department of Mathematics, Chalmers University of Technology. The purpose of the workshop was to present new analytical developments and numerical methods for solutions of inverse problems. State-of-the-art and future challenges in solving inverse problems for a broad range of applications was also discussed. The contributions in this volume are reflective of these themes and will be beneficial to researchers in this area.