Distribution of points of interpolation of multipoint Padé approximants

Abstract

A meshless multi-point flux approximation method AIP Conf.A variational approach to the theory of multipoint Padé approximants Abstract. In the present paper, we consider m 1 -almost uniform convergence of sequences of multipoint Padé approximants of degree (n, m n ), where m n = o(n/ log n). We provide a sufficient condition for the interpolation points to be uniformly distributed with respect to the equilibrium measure of the supporting compactum.

Distribution of Points of Interpolation and of Zeros of Exactly Maximally Convergent Multipoint Padé Approximants

“…The main result of the present paper is with a fixed number of the free poles (see [15]). Finally, in [16] the case was considered, when the degrees of the denominators tended slowly to infinity, namely, .…”

Distribution of points of interpolation and of zeros of exact maximally convergent multipoint Padé approximants

“…The case of polynomial interpolation of an arbitrary function f holomorphic in E was considered by R. Grothmann ([5]); he established the existence of an appropriate sequence Λ such that µ ωn −→ µ E , n → ∞, n ∈ Λ, respectively the balayage measures onto ∂E. Grothmann's result was generalized in relation to multipoint Padé approximants π β,f n,m with a fixed number of the free poles (see [9]). Finally, in [1] was considered the case when the degrees of the denominators tend slowly to infinity, namely m n = o(n/ ln n).…”

“…Consider the function φ, harmonic in A Γ,γ and φ := 0, Γ, min(0, − min t∈γ (U µ (t) − U ω (t)) + (U µ (z) − U ω (z)), γ From ( 7) and (9), we arrive at lim sup F n (z) ≤ φ, for z in A Γ,γ . Being harmonic, φ obeys the maximum and the minimum principles in this region.…”