Linear Operator Equations Approximation And Regularization
Download Linear Operator Equations Approximation And Regularization full books in PDF, epub, and Kindle. Read online free Linear Operator Equations Approximation And Regularization ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: M. Thamban Nair |
Publisher |
: World Scientific |
Total Pages |
: 264 |
Release |
: 2009 |
ISBN-10 |
: 9789812835659 |
ISBN-13 |
: 9812835652 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Linear Operator Equations by : M. Thamban Nair
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be. This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Author |
: M Thamban Nair |
Publisher |
: World Scientific |
Total Pages |
: 264 |
Release |
: 2009-05-05 |
ISBN-10 |
: 9789814469678 |
ISBN-13 |
: 981446967X |
Rating |
: 4/5 (78 Downloads) |
Synopsis Linear Operator Equations: Approximation And Regularization by : M Thamban Nair
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Author |
: Mark Anthony Lukas |
Publisher |
: |
Total Pages |
: 290 |
Release |
: 1981 |
ISBN-10 |
: OCLC:222142145 |
ISBN-13 |
: |
Rating |
: 4/5 (45 Downloads) |
Synopsis Regularization of Linear Operator Equations by : Mark Anthony Lukas
Author |
: M. Zuhair Nashed |
Publisher |
: |
Total Pages |
: 37 |
Release |
: 1973 |
ISBN-10 |
: OCLC:227533794 |
ISBN-13 |
: |
Rating |
: 4/5 (94 Downloads) |
Synopsis Approximate Regularized Solutions to Linear Operator Equations when the Data-vector is Not in the Range of the Operator by : M. Zuhair Nashed
The paper addresses itself to the problem of approximate pseudo solutions of the linear operator equation Af = g, when g is not necessarily in the range of the operator A. (Modified author abstract).
Author |
: Anatoly B. Bakushinsky |
Publisher |
: Walter de Gruyter GmbH & Co KG |
Total Pages |
: 447 |
Release |
: 2018-02-05 |
ISBN-10 |
: 9783110556384 |
ISBN-13 |
: 3110556383 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Regularization Algorithms for Ill-Posed Problems by : Anatoly B. Bakushinsky
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 |
: V. V. Vasin |
Publisher |
: Walter de Gruyter |
Total Pages |
: 268 |
Release |
: 2013-02-18 |
ISBN-10 |
: 9783110900118 |
ISBN-13 |
: 3110900114 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Ill-Posed Problems with A Priori Information by : V. V. Vasin
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Author |
: Andreas Neubauer |
Publisher |
: |
Total Pages |
: 104 |
Release |
: 1986 |
ISBN-10 |
: 3853696376 |
ISBN-13 |
: 9783853696378 |
Rating |
: 4/5 (76 Downloads) |
Synopsis Tikhonov-regularization of Ill-posed Linear Operator Equations on Closed Convex Sets by : Andreas Neubauer
Author |
: Vitalii P. Tanana |
Publisher |
: Walter de Gruyter GmbH & Co KG |
Total Pages |
: 168 |
Release |
: 2018-03-19 |
ISBN-10 |
: 9783110575835 |
ISBN-13 |
: 3110575833 |
Rating |
: 4/5 (35 Downloads) |
Synopsis Optimal Methods for Ill-Posed Problems by : Vitalii P. Tanana
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 |
: V. P. Tanana |
Publisher |
: Walter de Gruyter |
Total Pages |
: 229 |
Release |
: 2012-02-13 |
ISBN-10 |
: 9783110900156 |
ISBN-13 |
: 3110900157 |
Rating |
: 4/5 (56 Downloads) |
Synopsis Methods for Solving Operator Equations by : V. P. Tanana
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Author |
: Thomas Schuster |
Publisher |
: Walter de Gruyter |
Total Pages |
: 296 |
Release |
: 2012-07-30 |
ISBN-10 |
: 9783110255720 |
ISBN-13 |
: 3110255723 |
Rating |
: 4/5 (20 Downloads) |
Synopsis Regularization Methods in Banach Spaces by : Thomas Schuster
Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.