Linear Operator Equations Approximation And Regularization

Author : M. Thamban Nair
Publisher : World Scientific
ISBN 13 : 9812835652
Total Pages : 264 pages
Book Rating : 4.59/5 ( download)

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Download or read book Linear Operator Equations written by M. Thamban Nair and published by World Scientific. This book was released on 2009 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 981446967X
Total Pages : 264 pages
Book Rating : 4.78/5 ( download)

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Download or read book Linear Operator Equations: Approximation And Regularization written by M Thamban Nair and published by World Scientific. This book was released on 2009-05-05 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.45/5 ( download)

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Download or read book Regularization of Linear Operator Equations written by Mark Anthony Lukas and published by . This book was released on 1981 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : M. Zuhair Nashed
Publisher :
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.94/5 ( download)

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Download or read book Approximate Regularized Solutions to Linear Operator Equations when the Data-vector is Not in the Range of the Operator written by M. Zuhair Nashed and published by . This book was released on 1973 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : V. V. Vasin
Publisher : Walter de Gruyter
ISBN 13 : 3110900114
Total Pages : 268 pages
Book Rating : 4.18/5 ( download)

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Download or read book Ill-Posed Problems with A Priori Information written by V. V. Vasin and published by Walter de Gruyter. This book was released on 2013-02-18 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Anatoly B. Bakushinsky
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110556383
Total Pages : 342 pages
Book Rating : 4.84/5 ( download)

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Download or read book Regularization Algorithms for Ill-Posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Andreas Neubauer
Publisher :
ISBN 13 : 9783853696378
Total Pages : 104 pages
Book Rating : 4.76/5 ( download)

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Download or read book Tikhonov-regularization of Ill-posed Linear Operator Equations on Closed Convex Sets written by Andreas Neubauer and published by . This book was released on 1986 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Vitalii P. Tanana
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110575833
Total Pages : 138 pages
Book Rating : 4.35/5 ( download)

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Download or read book Optimal Methods for Ill-Posed Problems written by Vitalii P. Tanana and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-03-19 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 3110900157
Total Pages : 229 pages
Book Rating : 4.56/5 ( download)

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Download or read book Methods for Solving Operator Equations written by V. P. Tanana and published by Walter de Gruyter. This book was released on 2012-02-13 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : MANSUK SONG
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.38/5 ( download)

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Download or read book REGULARIZATION-PROJECTION METHODS AND FINITE-ELEMENT APPROXIMATIONS FOR ILL-POSED LINEAR OPERATOR EQUATIONS.. written by MANSUK SONG and published by . This book was released on 1978 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: