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Some Good Sequences of Interpolatory Polynomials: Addendum

Published online by Cambridge University Press:  20 November 2018

G. Freud  and
A. Sharma
G. Freud
Affiliation:
Ohio State University, Columbus, Ohio
A. Sharma
Affiliation:
University of Alberta, Edmonton, Alberta
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Extract

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In 1974 [2] we used the n + 2 zeros of (1 - x2)Pn(α, β)(x), α, β > — 1, where Pn(α, β)(x) denotes Jacobi polynomials, to construct a sequence of linear operators {An(α, β)(f, x)} which has the following properties:

(i) An(α, β)(f, x) is a linear polynomial operator mapping C[— 1, 1] into polynomials of degree ≦ n(1 + c), (c > 0 fixed but arbitrary)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1163 - 1166
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. de Voie, R., Degree of approximation, in Approximation Theory II (Academic Press, New York, 1976), 117–162.Google Scholar
2. Freud, G. and Sharma, A., Some good sequences of interpolator y polynomials, Can. J. Math. 26 (1974), 233–246.Google Scholar