# Accurate evaluation of the $k$-th derivative of a polynomial

1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-01146529
Contributor : Lip6 Publications <>
Submitted on : Tuesday, April 28, 2015 - 2:50:08 PM
Last modification on : Friday, May 24, 2019 - 5:28:26 PM

### Citation

Hao Jiang, Stef Graillat, Canbin Hu, Shengguo Lia, Xiangke Liao, et al.. Accurate evaluation of the $k$-th derivative of a polynomial. Journal of Computational and Applied Mathematics, Elsevier, 2013, 243, pp.28-47. ⟨10.1016/j.cam.2012.11.008⟩. ⟨hal-01146529⟩

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