✦ LIBER ✦

Landweber scheme for compact operator equation in Hilbert space and its applications

✍ Scribed by Qu, Gangrong ;Jiang, Ming

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 133 KB
Volume: 25
Category: Article
ISSN: 1069-8299
DOI: 10.1002/cnm.1196

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✦ Synopsis

Abstract

We study the Landweber scheme for linear compact operator equation in infinite Hilbert spaces. Using the singular value decomposition for compact operators, we obtain a formula for the Landweber scheme after n iterations and iterative truncated error and consequently establish its convergence conditions. Our results extend known results on convergence conditions. As applications, we apply the Landweber scheme to the X‐ray tomography and extrapolation of band‐limited functions, and establish accelerated strategies for each application. Copyright © 2008 John Wiley & Sons, Ltd.

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