Lagrange piecewise-quadratic interpolation based on planar unordered reduced data

Ryszard Kozera, P. Szmielew

Research output: Chapter in Book/Conference paperConference paper

Abstract

This paper discusses the problem of fitting non-parametric unordered reduced data (i. e. a collection of interpolation points) with piecewise-quadratic interpolation to estimate an unknown curve. in Euclidean space E-2. The term reduced data stands for the situation in which the corresponding interpolation knots are unavailable. The construction of ordering algorithm based on e-graph of points (i. e. a complete weighted graph using euclidean distances between points as respective weights) is introduced and tested here. The unordered set of input points is transformed into an ordered one upon using a minimal spanning tree (applicable for open curves). Once the order on points is imposed a piecewise-quadratic interpolation (gamma) over cap (2) combined with the so-called cumulative chords is used to fit unordered reduced data. The entire scheme is tested initially on sparse data. The experiments carried out for dense set of interpolation points and designed to test the asymptotics in. approximation by (gamma) over cap (2) result in numerically computed cubic convergence order gamma The latter coincides with already established asymptotics derived for gamma estimation via piecewise-quadratic interpolation based on ordered reduced data and cumulative chords.
Original languageEnglish
Title of host publicationComputer Information Systems and Industrial Management
EditorsK Saeed, W Homenda
PublisherSpringer-Verlag London Ltd.
Pages423-434
Number of pages12
ISBN (Electronic)978-3-319-24369-6
ISBN (Print)978-3-319-24368-9
DOIs
Publication statusPublished - 2015
Externally publishedYes
Event2015 International Conference on Computer Information Systems and Industrial Management Applications - Warsaw , Poland
Duration: 24 Sep 201526 Sep 2015

Publication series

NameLecture Notes in Computer Science
PublisherSpringer-Verlag
Volume9339
ISSN (Print)0302-9743

Conference

Conference2015 International Conference on Computer Information Systems and Industrial Management Applications
CountryPoland
CityWarsaw
Period24/09/1526/09/15

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