Re: ? ? ? ! ?
- To: mathgroup at smc.vnet.net
- Subject: [mg8328] Re: [mg8223] ? ? ? ! ?
- From: seanross at worldnet.att.net
- Date: Sun, 24 Aug 1997 13:24:44 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Lou Talman wrote:
>
> Can anyone explain what v3.0 of Mathematica thinks it's doing when it
> executes
>
> Plot[Abs'[x], {x, -3/10, 3/10}]
>
> ???
>
> Note the prime: The first argument of Plot was Abs'[x], not Abs[x].
>
> The strange behavior I see appears both on a PowerMac 7200/120 running
> Mac OS 7.5.3 and on a Wintel box running Windoze 95, so I presume that
> it isn't platform dependent--or at least, not fully so.
>
> --Lou Talman
Well, I understand what it is doing far away from zero. The Prime is
supposed to be derivative. It appears as though this method of calling
derivative generates an incorrect answer close to zero. The correct
answer should be a step function equaling +1 for positive x and -1 for
negative x and Complex Infinity at zero. Looking at a larger plot of
it, the fact that the "oscillations" are about 6% leads me to think that
the way the derivative is being taken is with some kind of Fourier
Transform and what we are seeing is Gibbs phenomena. There is about a
6% overshoot of any fourier transform at a step. You can see this on an
oscilloscope if you look at a square wave generator and you can
reproduce it on a computer if you take the fourier transform of a step
and then try and reconstruct the original function. There is nothing to
do to make the Gibbs phenomena go away. Putting more terms in your
fourier series makes the overshoots narrower. The only thing I could
fault wolfram is not including more terms in their series or not using
another method in this case.
Another case in point that no matter how well a numerical routine is
written, you never trust it implicitly without checking it out first.