Treffer: Exponentially convergent linear rational interpolation between equidistant (and other) points

A linear rational method to interpolate continuous functions on an interval \([a,b]\), is considered. The usual way of obtaining linear rational approximants is by fixing the denominator -- of degree \(n\) -- whose zeros must only depend on the selected interpolation points, and considering all the numerators with degree not greater than \(N\). The main purpose of the article is to demonstrate how the convergence of these interpolants -- with slowly increasing Lebesgue constants -- can be improved by decreasing \(n\) from \(N\), keeping the Lebesgue constant small. Two sections are devoted to the numerical solution of the corresponding computational problems.