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Find a rational interpolation of a function defined parametrically
gives the rational polynomial function of x, with numerator order m and denominator order n, that interpolates the curve with x and y coordinates fx and fy generated as a function of t, at the interpolation points t1,t2, ….
gives the rational interpolant with the interpolation points chosen automatically from the interval t0 to t1.
An approximation to the function whose graph is the upper half-circle:
The error is quite large near the endpoints:
Automatically chosen the interpolation points result in a smaller maximum error:
Wolfram Language 11.3 (March 2018) or above
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