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On approximation by trigonometric Lagrange interpolating polynomials

Published online by Cambridge University Press:  17 April 2009

T.F. Xie  and
S.P. Zhou
T.F. Xie
Affiliation:
Dalhousie UniversityDepartment of Math Stats and Computer ScienceHalifaxNova ScotiaCanada B3H 3J5
S.P. Zhou
Affiliation:
Dalhousie UniversityDepartment of Math Stats and Computer ScienceHalifaxNova ScotiaCanada B3H 3J5
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Abstract

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It is well-known that the approximation to f(x) ∈ C2π, by nth trigonometric Lagrange interpolating polynomials with equally spaced nodes in C2π, has an upper bound In(n)En(f), where En(f) is the nth best approximation of f(x). For various natural reasons, one can ask what might happen in Lp space? The present paper indicates that the result about the trigonometric Lagrange interoplating approximation in Lp space for 1 < p < ∞ may be “bad” to an arbitrary degree.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 3 , December 1989 , pp. 425 - 428
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Feng, Gongji, ‘Asymptotic expansion of the Lebesque constants associated with trigonometric interpolation corresponding to the equidistant nodal points’, Chinese, Math. Numer. Sinica 7 (1985), 420–425.Google Scholar
[2]Zygmund, A., Trigonometric Series (Cambridge University Press, Cambridge, 1959).Google Scholar