Accurate evaluation of the \(k\)-th derivative of a polynomial and its application
type: Item
instance of: scholarly article
title: Accurate evaluation of the \(k\)-th derivative of a polynomial and its application
zbMATH Open document ID: 1271.65040
author: Hao Jiang
author: Stef Graillat
author: Canbin Hu
author: Li-zhi Cheng
author: Fang Su
author: Shengguo Li
author: Xiang-Ke Liao
published in: Journal of Computational and Applied Mathematics
publication date: 2013-02-21T00:00:00Z
review text: A compensated algorithm for the evaluation of the \(k\)-th derivative of a polynomial in power basis is presented. The proposed algorithm makes the direct evaluation without obtaining the \(k\)-th derivative expression of the polynomial itself possible, 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 presented algorithm.
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 6138089
zbMATH Keywords: derivative evaluation
zbMATH Keywords: rounding error
zbMATH Keywords: compensated algorithm
zbMATH Keywords: floating-point arithmetic
zbMATH Keywords: error-free transformation
zbMATH Keywords: dereivative of a polynomial
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.cam.2012.11.008
OpenAlex ID: W2063715144
DOI: 10.1016/J.CAM.2012.11.008
description: scientific article; zbMATH DE number 6138089