Fractal polynomial interpolation
type: Item
instance of: scholarly article
title: Fractal polynomial interpolation
zbMATH Open document ID: 1082.28006
DOI: 10.4171/ZAA/1248
author: María Antonia Navascués
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2006-03-10T00:00:00Z
review text: Summary: A general procedure to define non-smooth versions of classical approximants by means of fractal interpolation functions is proposed. A complete and explicit description in the frequency domain of the functions constructed is obtained through their exact Fourier transforms. In particular, the generalization of the polynomial interpolation is developed. The Lagrange basis of the space of polynomials of degree lower or equal than \(N\) is generalized to a basis of fractal polynomials. As a consequence of the process, the density of the polynomial fractal interpolation functions with non-null scale vector in the space of continuous functions in a compact interval is deduced. Furthermore, a method for the interpolation of real data is proposed, by the construction of a fractal function coming from any classical approximant. The convergence of the process when the partition is refined is proved, supposing the convergence of the smooth interpolant.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 5011363
zbMATH Keywords: iterated function systems
zbMATH Keywords: fractal interpolation functions
zbMATH Keywords: polynomial interpolation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/1248
OpenAlex ID: W2028234518
description: scientific article; zbMATH DE number 5011363