Stable Approximate Evaluation of Unbounded Operators

AvCharles W. Groetsch

Häftad, Engelska, 2006

Del 1894 i serien Lecture Notes in Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2006-10-27
Mått:155 x 235 x 9 mm
Vikt:230 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:133
Upplaga:2007
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540399421

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Recensioner i media

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. Leitao, 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)

Innehållsförteckning

Some Problems Leading to Unbounded Operators.- Hilbert Space Background.- A General Approach to Stabilization.- The Tikhonov-Morozov Method.- Finite-Dimensional Approximations.