The solution of many problems requires us to compute derivatives. Complex step differentiation is a method of computing the first derivative of a real function, which circumvents the problem of roundoff error found with typical finite difference approximations.
Rounding error and formula error as functions of step size 
is crucial: if is too large, the estimate of the derivative is poor, due to truncation error; if is too small, subtraction will cause large rounding errors. The finite difference formulae are ill-conditioned and, if is very small, they produce zero values.
Where it can be applied, complex step differentiation provides a stable and accurate method for computing 
Continue reading ‘Real Derivatives from Imaginary Increments’
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