Derivatives on HP 42S
08-21-2018, 12:34 AM (This post was last modified: 08-21-2018 12:47 AM by Thomas Klemm.)
Post: #7
 Thomas Klemm Senior Member Posts: 1,688 Joined: Dec 2013
RE: Derivatives on HP 42S
(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

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!
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 Messages In This Thread Derivatives on HP 42S - lrdheat - 08-20-2018, 03:03 AM RE: Derivatives on HP 42S - Thomas Klemm - 08-20-2018, 04:38 AM RE: Derivatives on HP 42S - Thomas Klemm - 08-20-2018, 07:43 AM RE: Derivatives on HP 42S - Albert Chan - 08-20-2018, 11:54 PM RE: Derivatives on HP 42S - lrdheat - 08-20-2018, 10:57 PM RE: Derivatives on HP 42S - Thomas Klemm - 08-20-2018, 11:43 PM RE: Derivatives on HP 42S - Thomas Klemm - 08-21-2018 12:34 AM RE: Derivatives on HP 42S - Thomas Klemm - 08-21-2018, 01:35 AM RE: Derivatives on HP 42S - lrdheat - 08-21-2018, 02:24 AM RE: Derivatives on HP 42S - Thomas Klemm - 08-21-2018, 06:14 AM RE: Derivatives on HP 42S - RMollov - 08-23-2018, 12:58 PM RE: Derivatives on HP 42S - lrdheat - 08-24-2018, 02:51 AM RE: Derivatives on HP 42S - Thomas Klemm - 08-24-2018, 05:52 AM RE: Derivatives on HP 42S - lrdheat - 08-25-2018, 05:19 PM RE: Derivatives on HP 42S - Albert Chan - 08-25-2018, 07:03 PM RE: Derivatives on HP 42S - Thomas Klemm - 08-25-2018, 06:05 PM RE: Derivatives on HP 42S - Thomas Klemm - 08-25-2018, 08:00 PM RE: Derivatives on HP 42S - Albert Chan - 08-25-2018, 09:20 PM RE: Derivatives on HP 42S - Thomas Klemm - 08-26-2018, 04:54 AM RE: Derivatives on HP 42S - Thomas Okken - 08-26-2018, 01:54 PM RE: Derivatives on HP 42S - lrdheat - 08-26-2018, 04:47 PM RE: Derivatives on HP 42S - Albert Chan - 08-26-2018, 08:39 PM RE: Derivatives on HP 42S - Thomas Klemm - 08-26-2018, 08:00 PM RE: Derivatives on HP 42S - Albert Chan - 08-29-2018, 01:52 PM

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