J Austral Math Soc Ser A 52 pp111--118, 1992.

On the Lebesesgue Function for Lagrange Interpolation with Equidistant Nodes

T. M. Mills and Simon J. Smith

Abstract

Properties of the Lesbesgue function associated with interpolation at the equidistant nodes

xk,n = k, k = 0, 1, 2, ..., n,

are investigated. In particular, it is proved that the relative maxima of the Lesbesgue function are strictly decreasing from the outside towards the middle of the interval [0, n], and upper and lower bounds, and an asymptotic expansion, are obtained for the smallest maximum when n is odd.

1991 AMS Subject Classification: primary 41A05, 41A10, 41A44, 41A60; secondary 65D05

Browse the article

Authors

T. M. Mills

Simon J. Smith

LaTrobe University College of Northern Victoria, P.O. Box 199, Bendigo, Victoria 3550, Australia.