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On the Lebesgue function for lagrange interpolation with equidistant nodes

Part of: Approximations and expansions Numerical approximation and computational geometry

Published online by Cambridge University Press:  09 April 2009

T. M. Mills  and
Simon J. Smith
T. M. Mills
Affiliation:
LaTrobe University College of Northern VictoriaP.O. Box 199 Bendigo, Victoria 3550, Australia
Simon J. Smith
Affiliation:
LaTrobe University College of Northern VictoriaP.O. Box 199 Bendigo, Victoria 3550, Australia
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Abstract

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Properties of the Lebesgue function associated with interpolation at the equidistant nodes , are investigated. In particular, it is proved that the relative maxima of the Lebesgue 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.

Keywords

Lagrange interpolationpolynomialsequidistant nodesLebesgue functionasymptotic expansion

MSC classification

Secondary: 41A05: Interpolation 41A10: Approximation by polynomials 41A44: Best constants 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 65D05: Interpolation
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 1 , February 1992 , pp. 111 - 118
Copyright
Copyright © Australian Mathematical Society 1992

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