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

✍ Scribed by Peter Junghanns; Giuseppe Mastroianni; Markus Seidel

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 353 KB
• Volume: 283
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200910088

✦ Synopsis

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)