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...@gmail.com> wrote: > On 05/03/2012 07:55 PM, Russ P. wrote: > > > > > On May 3, 10:30 am, someone<newsbo...@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... -- http://mail.python.org/mailman/listinfo/python-list
