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Stable Approximate Evaluation of Unbounded Operators

  • Charles W. Groetsch

Part of the Lecture Notes in Mathematics book series (LNM, volume 1894)

Table of contents

About this book

Introduction

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.

Keywords

Hilbert space approximation ill-posed problem inverse problem stabilization unbounded operator

Authors and affiliations

  • Charles W. Groetsch
    • 1
  1. 1.The Traubert ChairSchool of Science and Mathematics, The CitadelCharlestonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-39942-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-39942-1
  • Online ISBN 978-3-540-39943-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site