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

@article{c9211241b29842fdb5c8b7fa47625e66,

title = "High accuracy Hermite approximation for space curves in Rd",

abstract = "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].",

keywords = "Approximation order, Computer aided geometric design, Hermite approximation, High accuracy, Space curves",

author = "Abedallah Rababah",

year = "2007",

month = jan,

day = "15",

doi = "10.1016/j.jmaa.2006.02.054",

language = "English",

volume = "325",

pages = "920--931",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - High accuracy Hermite approximation for space curves in Rd

AU - Rababah, Abedallah

PY - 2007/1/15

Y1 - 2007/1/15

N2 - 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].

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].

KW - Approximation order

KW - Computer aided geometric design

KW - Hermite approximation

KW - High accuracy

KW - Space curves

UR - https://www.scopus.com/pages/publications/33750283277

UR - https://www.scopus.com/pages/publications/33750283277#tab=citedBy

U2 - 10.1016/j.jmaa.2006.02.054

DO - 10.1016/j.jmaa.2006.02.054

M3 - Article

AN - SCOPUS:33750283277

SN - 0022-247X

VL - 325

SP - 920

EP - 931

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -