Accurate evaluation of the kk-th derivative of a polynomial and its application

This paper presents a compensated algorithm for the evaluation of the kk-th derivative of a polynomial in power basis. The proposed algorithm makes it possible the direct evaluation without obtaining the kk-th derivative expression of the polynomial itself, with a very accurate result to all but the most ill-conditioned evaluation. Forward error analysis and running error analysis are performed by an approach based on the data dependency graph. Numerical experiments illustrate the accuracy and efficiency of the algorithm.