Derivatives on HP 42S

[Thomas Klemm]

(08-20-2018 11:54 PM)Albert Chan Wrote:  Also, Why use complex numbers to search real extremums ?

From The Complex-Step Derivative Approximation:

Quote:For a small discrete h, this can be approximated by

\(\frac{\partial f}{\partial x}\approx\frac{\Im[f(x + ih)]}{h}\)

We call this the complex-step derivative approximation. This estimate is not
subject to subtractive cancellation errors, since it does not involve a difference
operation. This constitutes a tremendous advantage over the finite-difference
approximations.

Since we search for stationary points we set:

\(\frac{\partial f}{\partial x}=0\)

Which we approximate with just:

\(\Im[f(x + ih)]=0\)

Cheers
Thomas

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This is why it's a pain point if a calculator claims to support complex numbers but does not implement all functions. Yes, I'm looking at you HP-35S!