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Linear Operator Equations

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 652/5 ( reviews)

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Book Synopsis Linear Operator Equations by : M. Thamban Nair

Download or read book Linear Operator Equations written by M. Thamban Nair. This book was released on 2009. 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.

Linear Operator Equations: Approximation And Regularization

2009-05-05 Mathematics
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Release : 2009-05-05
Genre : Mathematics
Kind : eBook
Book Rating : 67X/5 ( reviews)

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Book Synopsis Linear Operator Equations: Approximation And Regularization by : M Thamban Nair

Download or read book Linear Operator Equations: Approximation And Regularization written by M Thamban Nair. This book was released on 2009-05-05. 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.

Regularization of Linear Operator Equations

1981 Linear operators
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Release : 1981
Genre : Linear operators
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Regularization of Linear Operator Equations by : Mark Anthony Lukas

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

Approximate Regularized Solutions to Linear Operator Equations when the Data-vector is Not in the Range of the Operator

1973 Linear operators
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Release : 1973
Genre : Linear operators
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Approximate Regularized Solutions to Linear Operator Equations when the Data-vector is Not in the Range of the Operator by : M. Zuhair Nashed

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. This book was released on 1973. 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).

Regularization Algorithms for Ill-Posed Problems

2018-02-05 Mathematics
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Release : 2018-02-05
Genre : Mathematics
Kind : eBook
Book Rating : 383/5 ( reviews)

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Book Synopsis Regularization Algorithms for Ill-Posed Problems by : Anatoly B. Bakushinsky

Download or read book Regularization Algorithms for Ill-Posed Problems written by Anatoly B. Bakushinsky. This book was released on 2018-02-05. 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

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