numpy (matrix solver) - python vs. matlab

[someone]

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...