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Constructive Approximation

, Volume 2, Issue 1, pp 213–219 | Cite as

On the degree of complex rational approximation to real functions

  • A. L. Levin
Article
  • 33 Downloads

Abstract

Iff∈C[−1, 1] is real-valued, letE R mn (f) andE C mn (f) be the errors in best approximation tof in the supremum norm by rational functions of type (m, n) with real and complex coefficients, respectively. We show that formn−1≥0
$$\gamma _{mn} = \inf \{ {{E_{mn}^C (f)} \mathord{\left/ {\vphantom {{E_{mn}^C (f)} {E_{mn}^R (f)}}} \right. \kern-\nulldelimiterspace} {E_{mn}^R (f)}}:f \in C[ - 1,1]\} = \tfrac{1}{2}.$$

AMS (MOS) classification

Primary, 41A20 Primary, 41A50 Secondary, 41A44 

Key words and phrases

Chebyshev approximation Rational approximation 

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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • A. L. Levin
    • 1
  1. 1.Department of MathematicsEveryman's UniversityTel-AvivIsrael

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