Re: Linear algebra and machine precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg77163] Re: Linear algebra and machine precision*From*: David Bailey <dave at Remove_Thisdbailey.co.uk>*Date*: Tue, 5 Jun 2007 06:36:21 -0400 (EDT)*References*: <f40hja$6lh$1@smc.vnet.net>

Dmitry Garanin wrote: > Hi, > > 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? > > Best regards, > > Dmitry > > The phrase "64-bit" really refers to the addressing capabilities of the machine, data can be of various lengths. Machine precision Reals are stored with 64-bit precision in both environments. David Bailey http://www.dbaileyconsultancy.co.uk