The density of alternation points in rational approximation

Authors:
P. B. Borwein, A. Kroó, R. Grothmann and E. B. Saff

Journal:
Proc. Amer. Math. Soc. **105** (1989), 881-888

MSC:
Primary 41A20; Secondary 41A50

MathSciNet review:
948147

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Abstract: We investigate the behavior of the equioscillation (alternation) points for the error in best uniform rational approximation on . In the context of the Walsh table (in which the best rational approximant with numerator degree , denominator degree , is displayed in the th row and the th column), we show that these points are dense in , if one goes down the table along a ray above the main diagonal . A counterexample is provided showing that this may not be true for a subdiagonal of the table. In addition, a Kadec-type result on the distribution of the equioscillation points is obtained for asymptotically horizontal paths in the Walsh table.

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0948147-0

Keywords:
Rational approximation,
extreme points,
best approximants

Article copyright:
© Copyright 1989
American Mathematical Society