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

• Autores: Hao Jiang, Stef Graillat, Canbin Hu, Sheng-Guo Li, Xiang-Ke Liao, Li-Zhi Cheng, Fang Su
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 243, Nº 1, 2013, págs. 28-47
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.11.008
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• Resumen

  • 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.