ASYMPTOTICS OF THE BEST POLYNOMIAL APPROXIMATION OF |x|p AND OF THE BEST LAURENT POLYNOMIAL APPROXIMATION OF sgn (x) ON TWO SYMMETRIC INTERVALS
نویسنده
چکیده
We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best uniform polynomial approximation of |x| on two symmetric intervals. Note, that in addition, we get asymptotics for the polynomials themselves under a certain renormalization. Also, we solve a problem on asymptotics of the best approximation of sgn (x) on [−1,−a] ∪ [a, 1] by Laurent polynomials.
منابع مشابه
Polynomials of the best uniform approximation to sgn(x) on two intervals
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