Adaptive Robust Numerical Differentiation

Version 1.6 (166 ko) par John D'Errico
Numerical derivative of an analytically supplied function, also gradient, Jacobian & Hessian
32,5K téléchargements
Mise à jour 3 déc. 2014

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The DERIVESTsuite provides a fully adaptive numerical differentiation tool for both scalar and vector valued functions. Tools for derivatives (up to 4th order) of a scalar function are provided, as well as the gradient vector, directional derivative, Jacobian matrix, and Hessian matrix. Error estimates are provided for all tools.
DERIVEST provides a robust adaptive numerical differentiation (up to the fourth derivative) of a user supplied function, much as quad does for integration. It is semi-intelligent, trying to use that step size which minimizes its estimate of the uncertainty in the derivative.

High order methods are used, although full control is provided to the user when you want it. You can direct the order of the method to be used, the general class of difference method employed (forward, backward, or central differences), the number of terms employed in its generalized Richardson acceleration scheme, step sizes, etc.

Although you can not provide a user supplied tolerance, DERIVEST does return an estimate of its uncertainty in the final result.

For example, the derivative of exp(x), at x=1 is exp(1)==2.71828182845905. DERIVEST does quite well.

[d,err]=derivest(@(x) exp(x),1)
d =

err =

See the provided demos for many more examples.

Citation pour cette source

John D'Errico (2024). Adaptive Robust Numerical Differentiation (, MATLAB Central File Exchange. Récupéré le .

Compatibilité avec les versions de MATLAB
Créé avec R14SP1
Compatible avec toutes les versions
Plateformes compatibles
Windows macOS Linux
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Version Publié le Notes de version

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Repaired problem when the point to evaluate the derivative happens to be the same as the period of a periodic function.