🚀 go-pugleaf

David Hough writes:
 > Part of the problem is that the benchmark programs in use measure only
 > common cases.  Various versions of the Linpack benchmark all have in common
 > that the data is taken from a uniform random distribution, producing problems
 > of very good condition.   So the worst possible linear
 > equation solver algorithm running on the dirtiest possible floating-point
 > hardware should be able to produce a reasonably small residual, even for
 > input problems of very large dimension.
 > 
In article <9106120131.AA20868@ucbvax.Berkeley.EDU> jbs@WATSON.IBM.COM writes:
 >          This is untrue.  Consider pivoting on the column element of
 > smallest magnitude while using IEEE single precision.  I don't believe
 > n has to be very large before you are in big trouble.

But you can get reasonable results without any pivoting if the condition
is very good!  Of course, if you do pivot you probably will get better
results; if you do full pivoting you will probably get still better results.

From my experience, once I wrote a solver where due to a coding error no
pivoting was performed any time.  It solved the 1024x1024 systems I initially
tested it on very well.  Of course, those systems were extremely good
conditioned.  The algorithm fell flat on its face when it was fed a not
so random input.
--
dik t. winter, cwi, amsterdam, nederland
dik@cwi.nl