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Eigenvalues in Mathematica 6.0.0 are SLOW

• To: mathgroup at smc.vnet.net
• Subject: [mg75648] Eigenvalues in Mathematica 6.0.0 are SLOW
• From: Roman <rschmied at gmail.com>
• Date: Tue, 8 May 2007 05:41:32 -0400 (EDT)

Hello all,

I just installed Mathematica 6.0.0 on my old PowerBook to try it out,
before upgrading my work horse machine. Doing a few benchmarks, I
noticed that the Eigenvalues command has slowed down significantly,
although the help on Eigenvalues says "Last modified in 5".

In particular, compare this code for repeatedly computing the
eigenvalues of a full 1000x1000 random symmetric matrix:

A[n_] := (# + Transpose[#]) &[Table[Random[], {n}, {n}]]
With[{n = 1000, p = 5},
 Table[M = A[n]; Timing[Eigenvalues[M];][[1]], {p}]]

Using $Version = "5.2 for Mac OS X (February 24, 2006)" I get

{5.38169 Second, 5.38112 Second, 5.39718 Second, 5.38392 Second,
   5.38465 Second}

But using $Version = "6.0 for Mac OS X PowerPC (32-bit) (April 20,
2007)" I get

{32.2618, 32.2137, 31.7375, 32.9869, 31.8762}

which is about 6 times slower! (and has no units ;-)

Fortunately, when you use sparse matrices and diagonalize with ARPACK
(using "Method->Arnoldi"), there is no difference in evaluation time.

Does anyone have an idea about what could have changed? Maybe some
precision goal specifiers or so whose defaults have changed?

Cheers!
Roman.

• Follow-Ups:
  • Re: Eigenvalues in Mathematica 6.0.0 are SLOW
    • From: Murray Eisenberg <murray@math.umass.edu>