A simple method for smoothing functions and compressing Hermite data
type: Item
instance of: scholarly article
title: A simple method for smoothing functions and compressing Hermite data
zbMATH Open document ID: 1070.65011
author: A. Mazroui
author: D. Sbibih
author: A. Tijini
published in: Advances in Computational Mathematics
publication date: 2005-05-20T00:00:00Z
review text: Consider a function \(f:[a,b] \to \mathbb R\) and a grid \(a = x_0 < x_1 < \cdots < x_n = b\). Assume that \(f \in C^k[x_i, x_{i+1}]\) for all \(i\) but \(f\) is only \(k_i\) times differentiable at the break point \(x_i\) (where \(k_i < k\)). The goal of the paper is to construct a function \(f_k \in C^k[a,b]\) that approximates \(f\), thus smoothing \(f\) at the points \(x_i\). This is achieved by a method based on a small modification of the concept of Bernstein polynomials. As an application, interpolatory splines in the Hermite sense can be computed in a recursive way, leading to a concept closely related to a multiresolution analysis. This allows to perform a data compression.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 2170077
zbMATH Keywords: smoothing of functions
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: data compression
zbMATH Keywords: interpolatory splines
zbMATH Keywords: multiresolution analysis
MaRDI profile type: Publication
full work available at URL: s10444-004-1783-y
OpenAlex ID: W2080773544
cites work: Q3034280
cites work: A practical guide to splines
cites work: Q4461995
cites work: Q4461996
cites work: A recursive construction of Hermite spline interpolants and applications
cites work: Q5589310
DOI: 10.1007/S10444-004-1783-Y
description: scientific article; zbMATH DE number 2170077