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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
Abstract 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)