Comonotone shape-preserving spline histopolation
type: Item
instance of: scholarly article
title: Comonotone shape-preserving spline histopolation
zbMATH Open document ID: 1114.65011
author: Malle Fischer
author: Peeter Oja
author: Helle Trossmann
published in: Journal of Computational and Applied Mathematics
publication date: 2007-01-22T00:00:00Z
review text: In this paper, the monotonicity preservation in histopolation problems is studied. Consider a mesh \( a = x_0 < x_1 < \ldots < x_n = b \) and let \( z_i, i = 1, \ldots , n \) be real numbers. The authors are interested in the construction of a \( C^1 \) function \( S \) on \([a,b]\) that for \( x \in [x_{i-1}, x_i]E, i = 1, \ldots , n \) is either a quadratic polynomial or a linear/linear rational function satisfying the histopolation conditions \[ \int^{x_i}_{x_{i-1}}ES(x) dx = z_i (x_i - x_{i-1}), \qquad i = 1, \ldots , n \] and boundary conditions \( S' (x_0) = \alpha, S' (x_n) = \beta \) or \( S(x_0) = \alpha, S(x_n) = \beta. \) The subintervals \( [x_{i-1}, x_i] \) are chosen to be rational or quadratic such that \( S(x) \) is comonotone shape preserving. It is shown that a unique comonotone histopolating spline exists for any histogramm having weak alternation of data on quadratic sections. For the general case a modification of the algorithm is proposed which consists in replacing some quadratic intervals by rational ones.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 5117672
zbMATH Keywords: rational spline
zbMATH Keywords: weak alternation of data
zbMATH Keywords: algorithm
reviewed by: Gerlind Plonka
MaRDI profile type: Publication
full work available at URL: j.cam.2005.12.010
OpenAlex ID: W2033555244
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DOI: 10.1016/J.CAM.2005.12.010
description: scientific article; zbMATH DE number 5117672