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

Authors:
Hao Jiang;Stef Graillat;Canbin Hu;Shengguo Li;Xiangke Liao;Lizhi Cheng;Fang Su
Affiliations:
School of Science, National University of Defense Technology, Changsha, 410073, China and The State Key Laboratory for High Performance Computation, National University of Defense Technology, Chan ...;PEQUAN, LIP6, Université Pierre et Marie Curie, CNRS, Paris, France;College of Electronic Science and Engineering, National University of Defense Technology, Changsha, 410073, China;School of Science, National University of Defense Technology, Changsha, 410073, China;School of Computer, National University of Defense Technology, Changsha, 410073, China;School of Science, National University of Defense Technology, Changsha, 410073, China and The State Key Laboratory for High Performance Computation, National University of Defense Technology, Chan ...;School of Science, National University of Defense Technology, Changsha, 410073, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

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.