Quadratic spline interpolation with coinciding interpolation and spline grids
type: Item
instance of: scholarly article
title: Quadratic spline interpolation with coinciding interpolation and spline grids
zbMATH Open document ID: 0554.41017
DOI: 10.1016/0771-050X(82)90008-0
author: Holger Mettke
author: Eckehard Pfeifer
author: Edward Neuman
published in: Journal of Computational and Applied Mathematics
publication date: 1982-01-01T00:00:00Z
review text: The authors consider the problem of quadratic spline interpolation of continuous functions in the case when the spline grid and the interpolation grid coincide. The main purpose of the paper is to deduce error estimations for the quadratic spline function s interpolating a given function f on a grid with width h. In order to obtain convergence procedures it is assumed that the function to be interpolated is suitably smooth or possesses a special behaviour. For example, if f' is of bounded variation then the interpolating spline s converges to f for arbitrary grid sequences. The same result is valid for functions of higher smoothness. The authors examine a best approximation property of quadratic interpolating splines. In the final part of the paper the authors find an approximation solution for a boundary value problem of first order by means of the collocation method using quadratic spline functions.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 3882954
zbMATH Keywords: quadratic spline interpolation
zbMATH Keywords: spline grid
zbMATH Keywords: interpolation grid
zbMATH Keywords: error estimations
zbMATH Keywords: collocation method
reviewed by: Dimitrie D. Stancu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3882954