numpy (matrix solver) - python vs. matlab

[Russ P.]

Yeah, I realized that I should rephrase my previous statement to
something like this:

For any *empirical* engineering or scientific work, I'd say that a
condition number of 1e6 is likely to be unacceptable.

I'd put finite elements into the category of theoretical and numerical
rather than empirical. Still, a condition number of 1e6 would bother
me, but maybe that's just me.

--Russ P.


On May 3, 3:21 pm, someone <newsbo... at gmail.com> wrote:
> On 05/03/2012 07:55 PM, Russ P. wrote:
>
>
>
> > On May 3, 10:30 am, someone<newsbo... at gmail.com>  wrote:
> >> On 05/02/2012 11:45 PM, Russ P. wrote:
> >>> For any practical engineering or scientific work, I'd say that a
> >>> condition number of 1e6 is very likely to be completely unacceptable.
>
> >> 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 say that the problem lies with the highest natural frequencies,
> >> they for sure cannot be verified - there's too little energy in them.
> >> But the lowest frequencies (the most important ones) are good, I think -
> >> even for high cond number.
>
> > Did you mention earlier what "FEM" stands for? If so, I missed it. Is
> > it finite-element modeling? Whatever the case, note that I said, "If
>
> Sorry, yes: Finite Element Model.
>
> > you are just doing pure mathematical or numerical work with no real-
> > world measurement error, then a condition number of
> > 1e6 may be fine." I forgot much more than I know about finite-element
> > modeling, but isn't it a purely numerical method of analysis? If that
>
> I'm not sure exactly, what is the definition of a purely numerical
> method of analysis? I would guess that the answer is yes, it's a purely
> numerical method? But I also thing it's a practical engineering or
> scientific work...
>
> > is the case, then my comment above is relevant.
>
> Uh, I just don't understand the difference:
>
> 1) "For any practical engineering or scientific work, I'd say that a
> condition number of 1e6 is very likely to be completely unacceptable."
>
> vs.
>
> 2) "If you are just doing pure mathematical or numerical work with no
> real-world measurement error, then a condition number of, 1e6 may be fine."
>
> I would think that FEM is a practical engineering work and also pure
> numerical work... Or something...
>
> > By the way, I didn't mean to patronize you with my earlier explanation
> > of orthogonal transformations. They are fundamental to understanding
> > the SVD, and I thought it might be interesting to anyone who is not
> > familiar with the concept.
>
> Don't worry, I think it was really good and I don't think anyone
> patronized me, on the contrary, people was/is very helpful. SVD isn't my
> strongest side and maybe I should've thought a bit more about this
> singular matrix and perhaps realized what some people here already
> explained, a bit earlier (maybe before I asked). Anyway, it's been good
> to hear/read what you've (and others) have written.
>
> Yesterday and earlier today I was at work during the day so
> answering/replying took a bit longer than I like, considering the huge
> flow of posts in the matlab group. But now I'm home most of the time,
> for the next 3 days and will check for followup posts quite frequent, I
> think...