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We consider the classical problem of finding the best uniform approximation by polynomials of 1/(x − a) 2 , where a > 1 is given, on the interval [−1, 1]. First, using symbolic computation tools we derive the explicit expressions of the poly-nomials of best approximation of low degrees and then give a parametric solution of the problem in terms of elliptic… (More)

Let Π d n+m−1 denote the set of polynomials in d variables of total degree less than or equal to n + m − 1 with real coefficients and let P(x), x = (x 1 ,. .. , x d), be a given homogeneous polynomial of degree n + m in d variables with real coefficients. We look for a polynomial p * ∈ Π d n+m−1 such that P − p * has least max norm on the unit ball and the… (More)

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