"Paul McGuire" <[EMAIL PROTECTED]> writes: > Dang, I thought I was testing the results sufficiently! What is the > accuracy problem? In my test cases, I've randomly created test > matrices, inverted, then multiplied, then compared to the identity > matrix, with the only failures being when I start with a singular > matrix, which shouldn't invert anyway.
There's a lot of ill-conditioned matrices that you won't hit at random, that aren't singular, but that are nonetheless very stressful for numerical inversion. The Hilbert matrix a[i,j]=1/(i+j+1) is a well known example. If you're taking exponential time to invert matrices (sounds like you're recursively using Cramer's Rule or something) that doesn't begin to be reasonable even for very small systems, in terms of accuracy as well as speed. It's a pure math construct that's not of much practical value in numerics. You might look at the Numerical Recipes books for clear descriptions of how to do this stuff in the real world. Maybe the experts here will jump on me for recommending those books since I think the serious numerics crowd scoffs at them (they were written by scientists rather than numerical analysts) but at least from my uneducated perspective, I found them very readable and well-motivated. -- http://mail.python.org/mailman/listinfo/python-list
