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

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

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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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