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## Re: LU - octave

 From: David Doolin Subject: Re: LU - octave Date: Mon, 17 Jan 2000 12:21:15 -0500

```In message <address@hidden>, "John W. E
aton" writes:
>On 17-Jan-2000, Igor Dukanovic <address@hidden> 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

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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