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Stable Approximate Evaluation of Unbounded Operators

  • Book
  • © 2007

Overview

Authors:
  1. Charles W. Groetsch

    1. The Traubert Chair, School of Science and Mathematics, The Citadel, Charleston, USA

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-X
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  2. Some Problems Leading to Unbounded Operators

    Pages 1-17

  3. Hilbert Space Background

    Pages 19-51

  4. A General Approach to Stabilization

    Pages 53-75

  5. The Tikhonov-Morozov Method

    Pages 77-99

  6. Finite-Dimensional Approximations

    Pages 101-119

  7. Back Matter

    Pages 121-131
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Keywords

About this book

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.

Reviews

From the reviews:

"This interesting monograph is devoted to the stable evaluation of the action of unbounded operators defined on Hilbert spaces. This problem is considered as an abstract mathematical problem within the scope of operator approximation theory. To motivate the discussion, the mathematical theory of inverse problems is briefly introduced. … The monograph is reasonably self-contained and elegantly written. It gradually invites the reader to learn more about the difficulties of solving ill-posed problems." (Antonio C. G. Leitão, Mathematical Reviews, Issue 2008 a)

“The author does an excellent job of covering the subject of the title in 120 pages and five chapters … . the monograph would make a nice graduate course or seminar in applied mathematics.” (John R. Cannon, SIAM Review, Vol. 52 (2), 2010)

Authors and Affiliations

  • The Traubert Chair, School of Science and Mathematics, The Citadel, Charleston, USA

    Charles W. Groetsch

Bibliographic Information

  • Book Title: Stable Approximate Evaluation of Unbounded Operators

  • Authors: Charles W. Groetsch

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/3-540-39942-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2007

  • Softcover ISBN: 978-3-540-39942-1Published: 27 October 2006

  • eBook ISBN: 978-3-540-39943-8Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 133

  • Topics: Operator Theory, Numerical Analysis

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