Re: PC problem alert
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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
>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
>stable up to the maximum size tested, 150x150. The SPARC station has shown
>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