# The best uniform quadratic approximation of circular arcs with high accuracy

Open Mathematics (2016)

• Volume: 14, Issue: 1, page 118-127
• ISSN: 2391-5455

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## Abstract

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In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.

## How to cite

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Abedallah Rababah. "The best uniform quadratic approximation of circular arcs with high accuracy." Open Mathematics 14.1 (2016): 118-127. <http://eudml.org/doc/276863>.

@article{AbedallahRababah2016,
abstract = {In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.},
author = {Abedallah Rababah},
journal = {Open Mathematics},
keywords = {Bézier curves; Quadratic best uniform approximation; Circular arc; High accuracy; Approximation order; Equioscillation; quadratic best uniform approximation; circular arc; high accuracy; approximation order; equioscillation},
language = {eng},
number = {1},
pages = {118-127},
title = {The best uniform quadratic approximation of circular arcs with high accuracy},
url = {http://eudml.org/doc/276863},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Abedallah Rababah
TI - The best uniform quadratic approximation of circular arcs with high accuracy
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 118
EP - 127
AB - In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.
LA - eng
KW - Bézier curves; Quadratic best uniform approximation; Circular arc; High accuracy; Approximation order; Equioscillation; quadratic best uniform approximation; circular arc; high accuracy; approximation order; equioscillation
UR - http://eudml.org/doc/276863
ER -

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