numpy (matrix solver) - python vs. matlab

[someone]

On 05/04/2012 05:52 AM, Steven D'Aprano wrote:
> On Thu, 03 May 2012 19:30:35 +0200, someone wrote:

>> So how do you explain that the natural frequencies from FEM (with
>> condition number ~1e6) generally correlates really good with real
>> measurements (within approx. 5%), at least for the first 3-4 natural
>> frequencies?
>
> I would counter your hand-waving ("correlates really good", "within
> approx 5%" of *what*?) with hand-waving of my own:

Within 5% of experiments of course.
There is not much else to compare with.

> "Sure, that's exactly what I would expect!"
>
> *wink*
>
> By the way, if I didn't say so earlier, I'll say so now: the
> interpretation of "how bad the condition number is" will depend on the
> underlying physics and/or mathematics of the situation. The
> interpretation of loss of digits of precision is a general rule of thumb
> that holds in many diverse situations, not a rule of physics that cannot
> be broken in this universe.
>
> If you have found a scenario where another interpretation of condition
> number applies, good for you. That doesn't change the fact that, under
> normal circumstances when trying to solve systems of linear equations, a
> condition number of 1e6 is likely to blow away *all* the accuracy in your
> measured data. (Very few physical measurements are accurate to more than
> six digits.)

Not true, IMHO.

Eigenfrequencies (I think that is a very typical physical measurement 
and I cannot think of something that is more typical) don't need to be 
accurate with 6 digits. I'm happy with below 5% error. So if an 
eigenfrequency is measured to 100 Hz, I'm happy if the numerical model 
gives a result in the 5%-range of 95-105 Hz. This I got with a condition 
number of approx. 1e6 and it's good enough for me. I don't think anyone 
expects 6-digit accuracy with eigenfrequncies.