V.A. Morozov
Regularization Methods for Ill-Posed Problems
Florida: CRC Press, 1993

This monograph presents the theory and methods of approximate solutions of basic classes of ill-posed problems. It develops an abstract approach that is characterized by the following: widespread use of methods of functional analysis; concentration on general necessory and sufficient conditions of solvability and unique solvability of corresponding problems. The basic methods discussed is the methods of psendosolutions. The main focus of the monograph is on the development of methods of approximation of pseudo solutions and on evaluating the accuracy of approximation algorithms. For wide class of regular ill-posed problems, conditions of optimality and optimality with respect to oder are found. Some questions of the efficiency of selection of regularization parameters are also discussed for both consistent and inconsistent operator equations.

The presentation is illustrated by a number of examples from approximation theory, theory of splines, and numerical differentiation and integration.

This book sehould be a useful recource for specialists in numerical analisys.