High accuracy Hermite approximation for space curves in Rd

Abedallah Rababah

doi:10.1016/j.jmaa.2006.02.054

High accuracy Hermite approximation for space curves in R^d

Abedallah Rababah

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

In this article, it is shown that a space curve in R^d can be approximated by a piecewise polynomial curve of degree m with order (m + 1) + ⌊ (m + 1) / (2 d - 1) ⌋ rather than m + 1. Moreover, we show that the optimal order (m + 1) + ⌊ (m - 1) / (d - 1) ⌋ is possible for a particular set of curves of nonzero measure. Analogous results were shown to be true for Taylor polynomial interpolation in [A. Rababah, High order approximation method for curves, Comput. Aided Geom. Design 12 (1995) 89-102].

Original language	English
Pages (from-to)	920-931
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	325
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2006.02.054
Publication status	Published - Jan 15 2007
Externally published	Yes

Keywords

Approximation order
Computer aided geometric design
Hermite approximation
High accuracy
Space curves

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2006.02.054

Cite this

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AB - In this article, it is shown that a space curve in Rd can be approximated by a piecewise polynomial curve of degree m with order (m + 1) + ⌊ (m + 1) / (2 d - 1) ⌋ rather than m + 1. Moreover, we show that the optimal order (m + 1) + ⌊ (m - 1) / (d - 1) ⌋ is possible for a particular set of curves of nonzero measure. Analogous results were shown to be true for Taylor polynomial interpolation in [A. Rababah, High order approximation method for curves, Comput. Aided Geom. Design 12 (1995) 89-102].

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