Linear operator equations approximation and regularization

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...

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Bibliographic Details
Main Author: Nair, M. Thamban
Format: eBook Book
Language:English
Published: New Jersey World Scientific Publishing Co. Pte. Ltd 2009
World Scientific
World Scientific Publishing Company
WORLD SCIENTIFIC
WSPC
Subjects:
Linear operators
Numerical & Computational Mathematics
Operator equations
Pure Mathematics
SCIENCE
Discrepancy Principle
Fredholm Integral Equations
Accelerated Methods
Well-Posed Problems
Source Conditions
Regularization Method
Ill-Posed Problems
Operator Equations
Projection Methods
Galerkin Method
Nystrom Method
Parameter Choice Strategy
ISBN:9789812835642, 9812835644, 9789812835659, 9812835652
Online Access:Get full text
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Summary: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.
Bibliography:Includes bibliographical references and index
ISBN:9789812835642
9812835644
9789812835659
9812835652
DOI:10.1142/7055