Stable Approximate Evaluation of Unbounded Operators

2007
ISBN: 978-3-540-39942-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1894, 133 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 230 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Groetsch, Charles W.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

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