Let Aρ denote the set of functions analytic in |z| < ρ but not on |z| ρ 1 < ρ < ∞ . Walsh proved that the difference of the Lagrange polynomial interpolant of f z ∈ Aρ and the partial sum of the Taylor polynomial of f converges to zero on a larger set than the domain of definition of f . In 1980, Cavaretta et al. have studied the extension of Lagrange interpolation, Hermite interpolation, and H...

The present survey collects some recent results on barycentric interpolation showing the similarity to the corresponding Lagrange (or polynomial) theorems. Namely we state that the order of the Lebesgue constant for barycentric interpolation is at least log n; we state a Grünwald–Marcinkiewicz type theorem for the barycentric case; moreover we define a Bernstein type process for the barycentric...