## 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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Verfasserangaben: Sergei V. Pereverzev, Eberhard Schock, Sergei G. Solodky urn:nbn:de:hbz:386-kluedo-7940 Preprints (rote Reihe) des Fachbereich Mathematik (299) Preprint Englisch 1998 1998 Technische Universität Kaiserslautern 03.04.2000 Complexity; Ill-Posed Problems ; Linear Integral Equations Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik 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] Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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