Stable Approximate Evaluation of Unbounded Operators

✍ Scribed by Charles W. Groetsch (auth.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 2007
Tongue: English
Leaves: 133
Series: Lecture Notes in Mathematics 1894
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.

✦ Table of Contents

Front Matter....Pages I-X
Some Problems Leading to Unbounded Operators....Pages 1-17
Hilbert Space Background....Pages 19-51
A General Approach to Stabilization....Pages 53-75
The Tikhonov-Morozov Method....Pages 77-99
Finite-Dimensional Approximations....Pages 101-119
Back Matter....Pages 121-131

✦ Subjects

Operator Theory; Numerical Analysis

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