Dear mathtalk,
        I write as regards a particular paper: Chaotic Relaxation, by
Chazan and Miranker, Linear Algebra and its Applications, Vol 2 No 2:
199-222, 1969.
	A proof to part (c) of their main theorem appears on pages 218-221.
Could you please assist, and explain the moves made by Chazan and
Miranker. I'm currently considering the bottom of page 219 and am at a
loss. I don't see how Chazan and Miranker can claim that we can select
k_i(n+1) such that the sign of x_i^}{n+1-k_i(n+1)} equals that of
b_i^1.
     	Actually, if you could please explain their proof to part (b),
that would be rather helpful also. As mentioned at
http://answers.google.com/answers/threadview?id=531867 , I think I've
managed to concoct my own proof. But, I would like to understand the
linear algebraic moves made by Chazan and Miranker.
	Many thanks,
	dvd

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Clarification of Question by dvd03-ga on 22 Jun 2005 09:48 PDT

Reason for doubting that we can choose k_i(n+1) such that 
sgn(x_i^{n+1-k_i(n+1)})=sgn(b_i^1) is as follows:

	We know that Bz = z+v.
	We know that all entries in v are non-negative.
	So for any entry z_i, we have that mutliplication of z by B cannot
decrease the value of z_i.
	But, if this is so, then what if some z_i is positive and b_i^1
(which is Chazan and Miranker's peculiar notation for b_{1i}) is
negative? z_i + v_i is also positive by the above. Indeed, k_i(n+1)
value can we possibly choose to get a negative entry?
	I'm at a loss!
	:-(

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Clarification of Question by dvd03-ga on 22 Jun 2005 09:49 PDT

Oops!

Indeed, WHAT k_i(n+1) value can we possibly choose to get a negative entry?

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Clarification of Question by dvd03-ga on 22 Jun 2005 10:46 PDT

The paper in question may be found at: http://www.doc.ic.ac.uk/~dvd03/cm.pdf

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Clarification of Question by dvd03-ga on 24 Jun 2005 05:02 PDT

Any thoughts?

Hi, dvd03-ga:

Thanks, I was hunting for a copy of the paper.  Their electronic
journal issues don't go back that far!

regards, mathtalk-ga

The link to your article is not available now. Can I take a look at it?

-fgace