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Best sextic approximation of circular arcs with thirteen equioscillations. (English) Zbl 1403.41009

Summary: We approximate a circular arc using a polynomial curve of degree 6. The approximation has least deviation from the \(x\)-axis and the error function is of degree 12; the error function equioscillates 13 times rather than the classical 8 times equioscillations that are mathematically guaranteed by the Borel and Chebyshev theorems without a method to find their approximation.

MSC:

41A50 Best approximation, Chebyshev systems
41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
65D17 Computer-aided design (modeling of curves and surfaces)
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