On May 3, 10:30 am, someone <newsbo...@gmail.com> wrote: > On 05/02/2012 11:45 PM, Russ P. wrote: > > > > > On May 2, 1:29 pm, someone<newsbo...@gmail.com> wrote: > > >>> If your data starts off with only 1 or 2 digits of accuracy, as in your > >>> example, then the result is meaningless -- the accuracy will be 2-2 > >>> digits, or 0 -- *no* digits in the answer can be trusted to be accurate. > > >> I just solved a FEM eigenvalue problem where the condition number of the > >> mass and stiffness matrices was something like 1e6... Result looked good > >> to me... So I don't understand what you're saying about 10 = 1 or 2 > >> digits. I think my problem was accurate enough, though I don't know what > >> error with 1e6 in condition number, I should expect. How did you arrive > >> at 1 or 2 digits for cond(A)=10, if I may ask ? > > > As Steven pointed out earlier, it all depends on the precision you are > > dealing with. 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. But you had better be using "double precision" (64- > > bit) floating point numbers (which are the default in Python, of > > course). Those have approximately 12 digits of precision, so you are > > in good shape. Single-precision floats only have 6 or 7 digits of > > precision, so you'd be in trouble there. > > > 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 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 is the case, then my comment above is relevant. 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. -- http://mail.python.org/mailman/listinfo/python-list
