Re: PC problem alert

[DSOUTH[ AT ]uoft02.utoledo.edu]

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 >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.
 I assume that the gestalts of the various PC's varied only in
 manufacture.  (a.k.a. They were all running the same DOS revision,
 TSR's, network/mouse/?? drivers).  Though other that the differences
 in BIOS, none of these would be a likely canidate for the type of
 numerical inaccuracies described.
 >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.
 Out of interest, were the matricies permuted with smaller elements
 to the upper-left-hand corner? If memory serves the "standard"
 implementation of the Householder reduction is preformed from the
 bottom-right corner -- large variations in element magnitude there
 will cause considerable rounding errors.
 >From these tests we conclude that MS Fortran itself is OK. The
 >problem might be specific to certain Compuadd machines but I
 >have heard related complaints about rounding errors from
 >colleagues so I suspect that it may be general to the Intel 286 chip.
 Well, if it is producing binaries that give large variations in
 results across supposedly "compatable" platforms, I might be a
 bit suspect about their math libraries "hardware dependance" (perhaps
 a check for the IEEE aproved accuracy??). But then again, I am a bit
 suspect of everyone's math libraries after reading Plauger's book.
 --
 /* Dale Southard Jr. -- Smith Research Group           Sr. Rigger      */
 /* Department of Chemistry                            AFF/I   SL/I     */
 /* University of Toledo                                  D-11216       */
 /* dsouth[ AT ]uoft02.utoledo.edu -- "Just another skydiving grad
 student." */