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Best approximation of polynomials on the sphere and on the ball. (English) Zbl 0994.41007

Haussmann, Werner (ed.) et al., Recent progress in multivariate approximation. Proceedings of the 4th international conference, Witten-Bommerholz, Germany, September 24-29, 2000. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 137, 23-30 (2001).
The authors compute the errors of best Chebychev polynomial approximation for several multivariate monomials in the \(m\)-dimensional Euclidean ball and the \(m\)-dimensional Euclidean sphere. The results are nontrivial, but a lot of work is still neccesary to close the problem for general monomials \(x_1^{a_1}\cdots x_m^{a_m}\).
For the entire collection see [Zbl 0972.00049].

MSC:

41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
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