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Article Dans Une Revue Journal of Computational and Applied Mathematics Année : 2013

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

Hao Jiang
Canbin Hu
  • Fonction : Auteur
Shengguo Lia
  • Fonction : Auteur
Xiangke Liao
  • Fonction : Auteur
Lizhi Cheng
  • Fonction : Auteur
Fang Su
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-01146529 , version 1 (28-04-2015)

Identifiants

Citer

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, 2013, 243, pp.28-47. ⟨10.1016/j.cam.2012.11.008⟩. ⟨hal-01146529⟩
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