Finite-part integrals and modified splines
type: Item
instance of: scholarly article
title: Finite-part integrals and modified splines
zbMATH Open document ID: 1074.65028
published in: BIT
publication date: 2005-04-07T00:00:00Z
review text: The authors recall a uniform convergence theorem for finite-part integrals, which are derivatives of weighted Cauchy principal value integrals. An example of a sequence of functions satisfying such a theorem is the sequence of complete cubic interpolatory splines. Approximating splines and optimal nodal splines based on locally uniform partitions do not satisfy the boundary conditions of the theorem. Therefore, after an introduction to these two classes of functions, a suitable two-stage process by modifying the splines and their derivatives at the end points of the integration interval is provided in such a way that all hypothesis of the uniform convergence theorem are satisfied. The splines so modified can now be used in the numerical evaluation of finite-part integrals.
reviewed by: Paola Lamberti
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 2153702
zbMATH Keywords: spline approximation
zbMATH Keywords: boundary conditions
zbMATH Keywords: finite-part integrals
zbMATH Keywords: uniform convergence
zbMATH Keywords: Cauchy principal value integrals
author: V. Demichelis
author: Philip Rabinowitz
MaRDI profile type: Publication
DOI: 10.1023/B:BITN.0000039419.61024.0D
description: scientific article; zbMATH DE number 2153702