Convergence orders in length estimation with exponential parameterization and ε -uniformly sampled reduced data

R. Kozera, Lyle Noakes, P. Szmielew

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    © 2016 NSP Natural Sciences Publishing Cor. We investigate the length approximation of the unknown regular curve in arbitrary Euclidean space upon applying a piecewise-quadratic interpolation based on ε -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.
    Original languageEnglish
    Pages (from-to)107-115
    JournalApplied Mathematics and Information Sciences
    Volume10
    Issue number1
    DOIs
    Publication statusPublished - 2016

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