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Ray Sequences of Best Rational Approximants For |x|α

Published online by Cambridge University Press:  20 November 2018

E. B. Saff  and
H. Stahl
E. B. Saff
Affiliation:
Institute for Constructive Mathematics Department of Mathematics University of South Florida Tampa, Florida 33620 U.S.A.
H. Stahl
Affiliation:
TFH/FB2 Luxemburger Str. 10 D-1000 Berlin 65 Germany
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Abstract

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The convergence behavior of best uniform rational approximations with numerator degree m and denominator degree n to the function |x|α, α > 0, on [-1, 1] is investigated. It is assumed that the indices (m, n) progress along a ray sequence in the lower triangle of the Walsh table, i.e. the sequence of indices {(m, n)} satisfies

In addition to the convergence behavior, the asymptotic distribution of poles and zeros of the approximants and the distribution of the extreme points of the error function on [-1, 1] will be studied. The results will be compared with those for paradiagonal sequences (m = n + 2[α/2]) and for sequences of best polynomial approximants.

Keywords

41A2541A44Walsh tablerational approximationbest approximationdistribution of poles and zeros
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 5 , 01 October 1997 , pp. 1034 - 1065
Copyright
Copyright © Canadian Mathematical Society 1997

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