On the convergence of some quadrature rules for Cauchy principal-value and finite-part integrals

Tsamasphyros, G; Theocaris, PS

dc.contributor.author	Tsamasphyros, G	en
dc.contributor.author	Theocaris, PS	en
dc.date.accessioned	2014-03-01T01:06:11Z
dc.date.available	2014-03-01T01:06:11Z
dc.date.issued	1983	en
dc.identifier.issn	0010-485X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9215
dc.subject	AMS Subject Classifications: Primary 65D30, 65D32, secondary 41A55	en
dc.subject	Cauchy-principal values	en
dc.subject	convergence	en
dc.subject	finite-part integrals	en
dc.subject	Jacobi quadratures	en
dc.subject	Lagrange polynomials	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	MATHEMATICAL TECHNIQUES	en
dc.title	On the convergence of some quadrature rules for Cauchy principal-value and finite-part integrals	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF02259907	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF02259907	en
heal.language	English	en
heal.publicationDate	1983	en
heal.abstract	In this paper sufficient conditions are derived to ensure the convergence of the Elliott and Hunter types of quadrature rules for the evaluation of weighted Cauchy principal-value integrals of the form:[Figure not available: see fulltext.] The simultaneous convergence in the interval (-1, 1) of both quadratures was established for a class of Hölder-continuous functions f(f∈Hμ). Corrections of some previous statements on the subject of convergence of such quadratures are also included. Moreover, a simple derivation of the Hunter and Elliott types of quadrature rules for the evaluation of the derivative of the p-th-order of the abovestated integral was given and sufficient conditions for the convergence of the Hunter-type quadrature were obtained. Thus, the convergence of this integral was ensured for functions f such that f(p)∈Hμ. © 1983 Springer-Verlag.	en
heal.publisher	Springer-Verlag	en
heal.journalName	Computing	en
dc.identifier.doi	10.1007/BF02259907	en
dc.identifier.isi	ISI:A1983RL81600002	en
dc.identifier.volume	31	en
dc.identifier.issue	2	en
dc.identifier.spage	105	en
dc.identifier.epage	114	en