Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509664 | Journal of Computational and Applied Mathematics | 2005 | 16 Pages |
Abstract
The interrelation of alternation points for the minimal error function and poles of best Chebyshev approximants is investigated if uniform approximation on the interval [-1,1] by rational functions of degree (n(s),m(s)) is considered, sâN. In general, the alternation points need not to be uniformly distributed with respect to the equilibrium measure on [-1,1], even not to be dense on the interval. We show that, at least for a subsequence ÎâN, the asymptotic behaviour of the alternation points to the degrees (n(s),m(s)),sâÎ, is completely determined by the location of the poles of the best approximants, and vice versa, if m(s)⩽n(s) or m(s)-n(s)=o(s/logs) as sââ.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Hans-Peter Blatt,