Stable Approximate Evaluation of Unbounded Operators [electronic resource] / by Charles W. Groetsch.

By:

Groetsch, Charles W [author.]

Contributor(s):

SpringerLink (Online service)

Material type: Text

TextSeries: Lecture Notes in Mathematics ; 1894Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Description: X, 133 p. online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783540399438

Subject(s):

Additional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification:

515.724 23

LOC classification:

QA329-329.9

Online resources:

Click here to access online

Contents:

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

In: Springer eBooksSummary: 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.

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

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.

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