PC problem alert

[Jack Houser <R1JJH-0at0-VM1.CC.UAKRON.EDU>]

 Dear Netters:
 A colleague discovered the following problem and suggested that I pass it
 on to the computational community, given the popularity of PCs.
 Jack Houser
 Department of Chemistry
 The University of Akron
 Akron, OH  44325-3601
 Subject: Numerical instabilities on PC's
 We have found mumerical instabilities for matrix diagonalizations on certain
 PC's.  The same Microsoft Fortran 5.1 double precision executable module was
 used on all PC's; Sun Fortran was used under UNIX on the SPARC station.
 Using a 111x111 relatively sparse matrix and a Jacobi rotation routine,
 a Compuadd 286 PC produced inaccurate eigenvalues. However, a Gateway 386 PC,
 a SPARC station IPC (UNIX) and the SPARC station running Microsoft Fortran
 under Soft-PC all produced correct results.  For this test the Gateway 386 was
 stable up to the maximum size tested, 150x150.  The SPARC station has shown no
 instability up to 550x550.
 Under previous tests, 3 different Compuadd 286 PC's all produced identical
 erroneous results.  These 286 PC's all produced accurate results for relatively
 small matrices.  But the inaccuracies began at some threshold matrix dimension
 (typically 40 to 100) and rapidly increased in magnitude until the results were
 unrecognizable.  Symptoms include failure to reproduce rigorous degeneracies
 and unnormalized eigenvectors.  The precise threshold depends on the nature of
 the matrix and on the particular diagonalization algorithm.  The faster
 Householder method is less stable than Jacobi rotations.
 From these tests we conclude that MS Fortran itself is OK. The problem might
 David Perry