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The best uniform quadratic approximation of circular arcs with high accuracy. (English) Zbl 1347.41008

Summary: 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 \(\theta = \pi/4\) arcs (quarter of a circle), the uniform error is \(5.5 \times 10^{-3}\). 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.

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
41A50 Best approximation, Chebyshev systems
65D17 Computer-aided design (modeling of curves and surfaces)
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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References:

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