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Subject: Re: An interesting numerical problem
Date: Thu, 22 Oct 2009 19:35:23 +0000 (UTC)
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"Yi Cao" <y.cao@cranfield.ac.uk> wrote in message <hbqb5s$9st$1@fred.mathworks.com>...
> "Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hbq6hb$5me$1@fred.mathworks.com>...
> > 
> > cond(P19*P19') is larger than 10^20. Eigen-space are highly parallel. The fact that P19 contains integer does not matter IMO because DET calculation using LU factorization.
> > 
> 
> For L*U = P*P', theoretically, L should be P and U should be P' because P is low triangular and P' is upper triangular.  Clearly, LU factorization in Matlab is not so smart.
> 
> Yi

IMO, its not so much that "Matlab is not so smart" as it is that due to 
floating point arithmetic, numerical problems and theoretical problems 
don't always agree.  In fact, you can even find "simple" cases where

(a + b) + c ~= a + (b + c)