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- Ionela Moale, Franz Peherstorfer
- Journal of Approximation Theory
- 2011

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 = (x1, . . . , xd ), 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 unit… (More)

- Ionela Moale, Franz Peherstorfer
- Journal of Approximation Theory
- 2011

Denote by Π 2 n+m−1 := { ∑ 0≤i+ j≤n+m−1 ci, j x i y j : ci, j ∈ R} the space of polynomials of two variables with real coefficients of total degree less than or equal to n + m − 1. Let b0, b1, . . . , bl ∈ R be given. For n, m ∈ N, n ≥ l + 1 we look for the polynomial b0x ym + b1x ym+1 + · · · + bl x n−l ym+l + q(x, y), q(x, y) ∈ Π 2 n+m−1, which has least… (More)

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

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