Resumen de Accurate evaluation of the k -th derivative of a polynomial and its application

Hao Jiang, Stef Graillat, Canbin Hu, Sheng-Guo Li, Xiang-Ke Liao, Li-Zhi Cheng, Fang Su

• This paper presents a compensated algorithm for the evaluation of the k-th derivative of a polynomial in power basis. The proposed algorithm makes it possible the direct evaluation without obtaining the k-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.