Numerical differentiation of approximated functions with limited order-of-accuracy deterioration
type: Item
instance of: scholarly article
zbMATH Open document ID: 1251.65022
DOI: 10.1137/100805807
published in: SIAM Journal on Numerical Analysis
publication date: 2012-08-23T00:00:00Z
full work available at URL: CaltechAUTHORS:20121204-113815559
Mathematics Subject Classification ID: 65D25
zbMATH DE Number: 6070631
zbMATH Keywords: numerical differentiation
zbMATH Keywords: Chebyshev approximation
zbMATH Keywords: differentiation of approximated functions
zbMATH Keywords: numerical examples
zbMATH Keywords: domain decomposition
zbMATH Keywords: radial basis function methods
MaRDI profile type: Publication
OpenAlex ID: W2081921496
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title: Numerical differentiation of approximated functions with limited order-of-accuracy deterioration
author: O. Bruno
author: D. Hoch
review text: In many numerical applications such as the numerical solution of (partial) differential equations, the question of approximating and differentiating the underlying functions numerically arises. Since certain orders of the solution methods (e.g., of the partial differential equation) are desired, there should be no or minimal loss of accuracy during the process of the numerical differentiation. This is the theme of the current paper where new methods are proposed for exactly this purpose; the authors use Chebyshev approximations (Chebyshev interpolants) to minimise the loss of accuracy during the differentiation process. The errors that can arise in these new methods are analysed and upper bounds are provided. To show the usefulness of the ideas, numerical examples, domain decomposition approaches and comparisons with radial basis function methods are given.
reviewed by: Martin D. Buhmann
description: scientific article; zbMATH DE number 6070631