Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!mailrus!uwm.edu!uakari.primate.wisc.edu!gem.mps.ohio-state.edu!rpi!batcomputer!kahn
From: kahn@batcomputer.tn.cornell.edu (Shahin Kahn)
Newsgroups: comp.arch
Subject: Re: 1000000x1000000 Matrix (was: linpack)
Message-ID: <9118@batcomputer.tn.cornell.edu>
Date: 22 Oct 89 23:07:29 GMT
References: <9089@batcomputer.tn.cornell.edu> <46500082@uxe.cso.uiuc.edu>
Organization: Theory Center, Cornell U., Ithaca NY
Lines: 34

In article <46500082@uxe.cso.uiuc.edu> mcdonald@uxe.cso.uiuc.edu writes:
>I heartily agree with that: I have two projects that I tried on 
>a big supercomputer: one diagonalized zillions of 20x20 matrices,
>the other wants to diagonalize a single 1000000x1000000 matrix.
>Neither was suitable for a Cray!

Perhaps you could use a different algorithm to diagonalize
many 20x20 matrices.  It sounds like the kind of thing that
could be re-written with significant improvement.  
Like I was going to say in response to Eugene,  you  cant get
behind the wheels of a Ferarri, go to the school zone, and 
complain that you cant go faster than 25MPH!
If you have lots of scalar code (or code that doesnt run very fast
on a super), and if it can't be rewritten, all you are doing
is announcing *your* departure from supercomputers.  There will
always be applications that need the combination of speed, memory size,
memory bandwidth, IO bandwidth, disk size, the number
of users supported, etc. that only supers provide.  Yes, as advances
are made, a super will be just a smart way of integrating off-the-shelf
components rather than desiging the whole machine from scratch 
(although, as someone else pinted out, there is something to be said 
about total re-designs).
And dont assume for a second that those who make supers have not
noticed this!

But that's not really the point of this posting!!   My real question is:

1) Is your 1000000x1000000 matrix dense?  If not, how sparse is it?
2) How did you solve it?
3) On what machine did you solve it?
4) What is the application?  (Its not a complex matrix, is it?!)
 
Finally, I dont see why *any* micro would be better at this one
than a super?!