Implementing the derivative in C/C++

Question

How is the derivative of a f(x) typically calculated programmatically to ensure maximum accuracy?

I am implementing the Newton-Raphson method, and it re

Answer 1

In addition to John D. Cooks answer above it is important not only to take into account the floating point precision, but also the robustness of the function f(x). For instance, in finance, it is a common case that f(x) is actually a Monte Carlo-simulation and the value of f(x) has some noise. Using a very small step size can in these cases severely degrade the accuracy of the derivative.

Answer 2

What do you know about f(x)? If you only have f as a black box the only thing you can do is to numerically approximate the derivative. But the accuracy is usually not that good.

You can do much better if you can touch the code that computes f. Try "automatic differentiation". There some nice libraries for that available. With a bit of library magic you can convert your function easily to something that computes the derivative automatically. For a simple C++ example, see the source code in this German discussion.