Adaptive Robust Numerical Differentiation

Numerical derivative of an analytically supplied function, also gradient, Jacobian & Hessian
Updated 3 Dec 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.

Cite As

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

MATLAB Release Compatibility
Created with R14SP1
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

Flag as a toolbox

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