|Source:||John Lewis, Boeing Computer Services, Seattle, Washington.|
|Discipline:||Simple counter examples to Hellerman and Rarick algorithm|
These three matrix patterns were designed by Grimes and Lewis to demonstrate the type of breakdowns that can occur with the P^4 ordering. They also demonstrate how the P^5 ordering avoids the same type of breakdowns.
The P^4 ordering reorders these matrices so that a zero is on the diagonal. JGL009 and JGL011 depend on fill-in during the factorization to provide a nonzero pivot when using Gaussian Elimination without pivoting. P^4 reorders RGG010 in such a way that a zero is placed on the diagonal and no fill occurs in that position leaving a ``structural'' zero for a pivot.
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Last change in this page: Wed Sep 22 13:33:33 US/Eastern 2004 [Comments: ]