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LP Approximation by Reciprocals of Trigonometric and Algebraic Polynomials

Published online by Cambridge University Press:  20 November 2018

Ronald A. Devore ,
D. Leviatan  and
Xiang Ming Yu
Ronald A. Devore
Affiliation:
Department of Mathematics Univ. of South Carolina Columbia, SC 29208 USA
D. Leviatan
Affiliation:
Raymond & Beverley Sackler Faculty of Exact Sciences Tel Aviv University Israel
Xiang Ming Yu
Affiliation:
Department of Mathematics Nanjing Normal University Nanjing P. R. of China
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Abstract

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We give an estimate for the error of Lp approximation by reciprocals of polynomials. These estimates are the analogues of the Jackson and Ditzian - Totik estimates for polynomial approximation.

Keywords

41A2541A20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 4 , 01 December 1990 , pp. 460 - 469
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Ditzian, Z. and Totik, V. Moduli of smoothness, Springer-Verlag, Berlin 1987.Google Scholar
2. Leviatan, D., Levin, A. L. and Saff, E. B. On approximation in the Lp-norm by reciprocals of polynomials, J. Approx. Theory 57 1989 322–331.Google Scholar
3. Lorentz, G. G. Approximation of functions, Holt Rinehart and Winston, New York, 1966.Google Scholar