numpy (matrix solver) - python vs. matlab

[Russ P.]

On May 2, 1:29 pm, someone <newsbo... at 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.