Ray Sequences of Best Rational Approximants For |x|α

Saff, E. B. ; Stahl, H.

Canadian journal of mathematics, Tome 49 (1997) no. 5, pp. 1034-1065

Résumé

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.

Détail

DOI : 10.4153/CJM-1997-052-3

Mots-clés : 41A25, 41A44, Walsh table, rational approximation, best approximation, distribution of poles and zeros

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