On the stabiity of collocation methods for Cauchy singular integral equations in weighted L  p    spaces | Zendy

Junghanns Peter | Zendy; Mastroianni Giuseppe | Zendy; Seidel Markus | Zendy

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On the stabiity of collocation methods for Cauchy singular integral equations in weighted L p spaces

Author(s) -

Junghanns Peter,

Mastroianni Giuseppe,

Seidel Markus

Publication year - 2010

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200910088

Subject(s) - mathematics , cauchy distribution , collocation (remote sensing) , singular integral , discretization , sequence (biology) , initial value problem , stability (learning theory) , interval (graph theory) , mathematical analysis , cauchy's integral formula , cauchy problem , integral equation , pure mathematics , combinatorics , remote sensing , machine learning , geology , biology , computer science , genetics

Necessary and sufficient conditions for the stability of certain collocation methods applied to Cauchy singular integral equations on an interval are presented for weighted L ' norms. Moreover, the behavior of the approximation numbers, in particular their so‐called k ‐splitting property, of the respective sequence of discretized operators is discussed (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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