Information Complexity of Multivariate Fredholm Equations in Sobolev Classes
- In this paper, the complexity of full solution of Fredholm integral equations of the second kind with data from the Sobolev class \(W^r_2\) is studied. The exact order of information complexity is derived. The lower bound is proved using a Gelfand number technique. The upper bound is shown by providing a concrete algorithm of optimal order, based on a specific hyperbolic cross approximation of the kernel function. Numerical experiments are included, comparing the optimal algorithm with the standard Galerkin method.
Author: | Karin Frank, Stefan Heinrich, Sergei Pereverzev |
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URN: | urn:nbn:de:hbz:386-kluedo-50629 |
Series (Serial Number): | Interner Bericht des Fachbereich Informatik (263) |
Document Type: | Report |
Language of publication: | English |
Date of Publication (online): | 2017/11/10 |
Year of first Publication: | 1995 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2017/11/10 |
Page Number: | 17 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Informatik |
DDC-Cassification: | 0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik |
Licence (German): | Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0) |