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 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.

This book is a very important contribution to `theoretical numerical analysis', it is very well written and contains also an introductory chapter on the basic ideas of functional analysis ... It is appropriate for students in a mathematical curriculum for a second level course in an MSc programme. --Prof Dr Eberhard Schock, University of Kaiserslautern, Germany

This well-written book could be used for an advanced undergraduate or early graduate course in (linear) numerical functional analysis. --Heinz W Engl, Austrian Academy of Sciences

This book is self-contained and easily accessible to researchers and students at the master's level who are used to the abstract setting of operator equations and regularization theory. --Mathematical Reviews