Adaptive Robust Numerical Differentiation

Numerical derivative of an analytically supplied function, also gradient, Jacobian & Hessian

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 =
2.71828182845904

err =
1.02015503167879e-14

See the provided demos for many more examples.