Convergence Orders in Length Estimation with Exponential Parameterization and e -Uniformly Sampled Reduced Data

Authors

Ryszard Kozera, Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences - SGGW, Nowoursynowska str. 159, 02-776 Warsaw, PolandFollow
Lyle Noakes, School of Mathematics and Statistics, The University ofWestern Australia, 35 Stirling Highway, CrawleyW.A. 6009, Perth, AustraliaFollow
Piotr Szmielew, Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences - SGGW, Nowoursynowska str. 159, 02-776 Warsaw, PolandFollow

Author Country (or Countries)

Poland

Abstract

We investigate the length approximation of the unknown regular curve in arbitrary Euclidean space upon applying a piecewise-quadratic interpolation based on e -uniformly sampled reduced data in combination with the exponential parameterization. As proved in this paper, similarly to the trajectory estimation, there is a discontinuity in the quality of length estimation with exponential parameterization performing no better than a blind uniform guess for the unknown knots, except for the case of cumulative chords. The theoretical asymptotic estimates established here for length approximation are also experimentally confirmed to be nearly sharp.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100110

Recommended Citation

Kozera, Ryszard; Noakes, Lyle; and Szmielew, Piotr (2016) "Convergence Orders in Length Estimation with Exponential Parameterization and e -Uniformly Sampled Reduced Data," Applied Mathematics & Information Sciences: Vol. 10: Iss. 1, Article 10.
DOI: http://dx.doi.org/10.18576/amis/100110
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss1/10