© 2007

Stable Approximate Evaluation of Unbounded Operators


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

Table of contents

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.


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

Authors and affiliations

  1. 1.The Traubert ChairSchool of Science and Mathematics, The CitadelCharlestonUSA

Bibliographic information

  • Book Title Stable Approximate Evaluation of Unbounded Operators
  • Authors Charles W. Groetsch
  • Series Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-540-39942-1
  • eBook ISBN 978-3-540-39943-8
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages X, 133
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Operator Theory
    Numerical Analysis
  • Buy this book on publisher's site


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)