Circularity of the Error Curve and Sharpness of the Cf Method in Complex Chebyshev Approximation *
نویسنده
چکیده
Let f(z) be analytic at the origin, and for e >0, let f(ez) be best approximated in the Chebyshev sense on the unit disk by a rational function of type (m, n). It has been shown previously by the CF method that the error curve for this approximation deviates from a circle by at most O(e 2m+2n+3) as e 0. We prove here that this bound is sharp in two senses: the error curve for a given function cannot be asymptotically more circular than the CF method predicts; moreover there exist functions for which the near-circularity is of order e 2m+2n+3 but no smaller.
منابع مشابه
Near-Circularity of the Error Curve In Complex Chebyshev Approximation
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