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Table of contents (5 chapters)
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
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