# 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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topAbedallah 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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