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Step size selection in numerical differences using a regression kink
KOSTYRKA, Andreï
2025
 

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Keywords :
numerical differentiation; error analysis; optimal step size; floating-point arithmetic; finite differences
Abstract :
[en] We propose a new step-size selection procedure for numerical differences based on fitting a piecewise linear shape to the observed estimate of truncation error and determining the position of its kink. The novelty of this method is in its use of the full information about the estimated total error behaviour at both sides around the optimum and in the incorporation of robust statistical tools for estimating the best V-shaped fit. The added safety checks ensure that the kink is detected if it exists, or a reasonable step size is returned in the case there is no kink. In numerical simulations, the proposed method algorithm outperforms two existing algorithms in terms of median error when tested on 5 well-behaved and 3 pathological functions.
Disciplines :
Quantitative methods in economics & management
Author, co-author :
KOSTYRKA, Andreï  ;  University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Department of Economics and Management (DEM)
Language :
English
Title :
Step size selection in numerical differences using a regression kink
Publication date :
15 May 2025
Number of pages :
11
Focus Area :
Computational Sciences
Commentary :
This method is implemented in the step.K() function in the pnd package (on CRAN) for the programming language R.
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since 15 May 2025

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