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On the efficient discretization of integral equations of the third kind

  • We propose a new discretization scheme for solving ill-posed integral equations of the third kind. Combining this scheme with Morozov's discrepancy principle for Landweber iteration we show that for some classes of equations in such method a number of arithmetic operations of smaller order than in collocation method is required to appoximately solve an equation with the same accuracy.

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Author:Sergei V. Pereverzev, Eberhard Schock, Sergei G. Solodky
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (299)
Document Type:Preprint
Language of publication:English
Year of Completion:1998
Year of Publication:1998
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Complexity; Ill-Posed Problems; Linear Integral Equations
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):45-XX INTEGRAL EQUATIONS / 45Axx Linear integral equations / 45A05 Linear integral equations
65-XX NUMERICAL ANALYSIS / 65Rxx Integral equations, integral transforms / 65R10 Integral transforms
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section {04 in that areag 68-00 General reference works (handbooks, dictionaries, bibliographies, etc.) / 68Qxx Theory of computing / 68Q25 Analysis of algorithms and problem complexity [See also 68W40]
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011