Estimates for best approximation to rational functions
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- by S. J. Poreda PDF
- Trans. Amer. Math. Soc. 159 (1971), 129-135 Request permission
Abstract:
Estimates for the deviation of certain rational functions and their polynomials of best uniform approximation on various sets are given. As a result, in some cases these deviation and polynomials are explicitly calculated. For example, the polynomials of best uniform approximation to the function $(\alpha z + \beta )/(z - a)(1 - \bar az),|a| \ne 1$, on the unit circle are given.References
- N. I. Ahiezer, Lekcii po Teorii Approksimacii, OGIZ, Moscow-Leningrad, 1947 (Russian). MR 0025598
- S. Ja. Al′per, Asymptotic values of best approximation of analytic functions in a complex domain, Uspehi Mat. Nauk 14 (1959), no. 1 (85), 131–134 (Russian). MR 0104826 S. J. Poreda, Best approximation to some rational functions, Thesis, University of Maryland, College Park, Md., 1970.
- T. J. Rivlin, Some explicit polynomial approximations in the complex domain, Bull. Amer. Math. Soc. 73 (1967), 467–469. MR 212193, DOI 10.1090/S0002-9904-1967-11785-3
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 159 (1971), 129-135
- MSC: Primary 30A82
- DOI: https://doi.org/10.1090/S0002-9947-1971-0291475-6
- MathSciNet review: 0291475