Influence of poles on equioscillation in rational approximation

  • H. P. Blatt


The error curve for the rational best approximation of ƒ ? C[?1, 1] is characterized by the well-known equioscillation property. Contrary to the polynomial case, the distribution of these alternations is not governed by the equilibrium distribution. It is known that these points need not be dense in [?1, 1]. The reason is the influence of the distribution of the poles of rational approximants. In this paper, we generalize the results known so far to situations where the requirements for the degrees of numerators and denominators are less restrictive.
How to Cite
Blatt, H. P. “Influence of Poles on Equioscillation in Rational Approximation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 1, Jan. 2006, pp. 3–11,
Research articles