Accurate function Sinc interpolation and derivative estimations over finite intervals

摘要

Function expansion in terms of finite Sinc bases is considered. For finite intervals, we considered proper transformation and weighted barycentric methods. We adjusted the transformation function to comply with the truncation of the expansion. This removes the unbounded behavior of the terminal derivatives and yields accurate results.Efficient weighted barycentric expansions are presented to improve the accuracies of function and derivative estimations. A new expression for the estimation of the second derivative is derived. The derived expressions are successfully applied to accurately locate the minimum of the solution and solve a singularly-perturbed problem.