Constructive Approximation

, Volume 6, Issue 1, pp 1–20

Fast decreasing polynomials

  • K. G. Ivanov
  • V. Totik

DOI: 10.1007/BF01891406

Cite this article as:
Ivanov, K.G. & Totik, V. Constr. Approx (1990) 6: 1. doi:10.1007/BF01891406


Matching two-sided estimates are given for the minimal degree of polynomialsP satisfyingP(0)=1 and ¦P(x)|≤exp(−ϕx¦)),x ∈ [−1,1], whereϕ is an arbitrary, in [0, 1], increasing function. Besides these fast decreasing polynomials we also consider bell-shaped polynomials and polynomials approximating well the signum function.

Key words and phrases

Algebraic polynomialsRate of decreaseInequalities

AMS classification


Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • K. G. Ivanov
    • 1
  • V. Totik
    • 2
  1. 1.Institute of MathematicsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Bolyai InstituteUniversity of SzegedSzegedHungary