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Step size selection in numerical differences using a regression kink

Author

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  • Andreï Kostyrka

    (DEM, Université du Luxembourg)

Abstract

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 algorithmoutperforms two existing algorithms in terms of median error when tested on 5 well-behaved and 3 pathological function

Suggested Citation

  • Andreï Kostyrka, 2025. "Step size selection in numerical differences using a regression kink," DEM Discussion Paper Series 25-09, Department of Economics at the University of Luxembourg.
    • Handle: RePEc:luc:wpaper:25-09
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    File URL: https://orbilu.uni.lu/handle/10993/64958
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    More about this item

    Keywords

    numerical differentiation; error analysis; optimal step size; floating-point arithmetic; finite differences.;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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