From help-octave-request at bevo dot che dot wisc dot edu  Mon Jan 17 11:21:37 2000
Subject: Re: LU - octave 
From: David Doolin <doolin at cs dot utk dot edu>
To: viveks at me dot iitb dot ernet dot in
cc: Igor Dukanovic <igor dot mat at uni-mb dot si>, help-octave@bevo.che.wisc.edu,         doolin@cs.utk.edu
Date: Mon, 17 Jan 2000 12:21:15 -0500

In message <14466 dot 54986 dot 126611 dot 645781 at tillamook-sharp dot bogus dot domain>, "John W. E
aton" writes:
>On 17-Jan-2000, Igor Dukanovic <igor dot mat at uni-mb dot si> wrote:
>
>| 
>| I'm used to the following LU-factorization
>| 
>| PA = LU,
>| 
>| and so the octave's choice seems good for me.
>
>This is the way Octave does it because it is the way Matlab does it.
>No doubt there would be some complaints if Octave's choice were any
>different.
>
>jwe

Several comments:  

Lapack was initially proposed by Demmel and Dongarra (lawn1 ---
lapack working note 1 available on netlib).

Demmel has co-authored pieces of Lapack software and the Lapack 
manual.

It turns out that a very beautiful proof of A = LU can be 
done inductively.  Demmel teaches it with complete pivoting:
PAP' = LU (Theorem 2.5, Applied Numerical Linear Algebra, Demmel,
1996).  Now an inductive proof may be beautiful in itself, but 
it turns out an algorithm for Gaussian Elimination is in
fact given by the induction step.  Clever, no?

Lapack extends Linpack, written in part by Dongarra and Cleve
Moler.   I am pretty sure Dongarra was a grad student with CM.
I am also pretty sure that CM == MathWorks == Matlab.

||P|| = 1  =>  P^T = P^{-1}, so there really isn't any 
inconsistency here: PA = LU  =>  A = P^TLU.

Matlab may or may not have distasteful inconsistencies, but 
this is not one of them.  

Thanks,

Dave D


>
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