Linear algebra and machine precision
- To: mathgroup at smc.vnet.net
- Subject: [mg77135] Linear algebra and machine precision
- From: Dmitry Garanin <dgaranin at yahoo.com>
- Date: Mon, 4 Jun 2007 03:57:59 -0400 (EDT)
I have Mathematica 5.0 on my laptop (Win XP pro 32 bit) and Mathematica 5.2 on my workstation (Win XP pro 64 bit). I have a program operating with eigensystems of huge matrices with nearly degenerate eigenvalues. The results become inaccurate on my laptop when I increase the size of the matrix while I always obtain accurate results on the workstation.
My initial thought was that on the workstation Mathematica uses longer machine numbers and that is why the results are accurate. However, $MachinePrecision outputs a number below 16 on both machines. Also computing 1-Sqrt(1+AVerySmallNumber) gives the same result on both machines. So that evidently Mathematica cannot really use those 64 bits. Or I understand something wrong?
Another explanation would be that linear algebra in Mathematica 5.0 is buggy.
BTW my program solving partial differential equations works well with Mathematica 5.0 but gives unstable results with Mathematica 5.2, so here the situation seems to be reversed.
What do you think?
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