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Re: Octave QR factorization


From: A S Hodel
Subject: Re: Octave QR factorization
Date: Wed, 17 Dec 2003 14:19:02 -0600

I am unable to access your script.  You should check

norm(Q*R - A)/norm(A), which will (typically) be around m*n*1e-15, where [m,n] = size(A).
You cannot expect perfect equality in numerical calculations.

Well, actually, you *can* expect it, but you'd be often disappointed by your results.

On Wednesday, December 17, 2003, at 02:04 PM, Bart Vandewoestyne wrote:

Hello Octave-list,

While I was checking the correctness of an exercise given to my students during one of my algebra exercise sessions, i found the following curiosity:

The purpose of the exercise was for students to calculate the QR factorization of a given matrix A. Now all I wanted to do is enter the factorization we found by hand into Octave and see if the product of Q and R is again the original matrix A.

What I found is that when I multiply the matrices Q and R we've found by hand and then check for Q*R==A, Octave tells me that Q*R is not equal to A, most probably due to rounding errors I guess...

If I run the same script in Matlab, Matlab *does* give me that Q*R=A... so it doesn't experience the rounding errors as much as Octave does???

So now my question is: why does Matlab gives different results than Octave? Is there a big difference in the implementation of QR between Matlab and Octave? Is there a way to decrease the rounding errors made by Octave so we get the same accuracy as Matlab?

The script I used can be found at http://www.cs.kuleuven.ac.be/~bartv/p370_oef1_6_17.m

When replying, please also reply to me personally, as I am not subscribed to the list...

Thanks,
Bart

--
Bart Vandewoestyne                    Bart.Vandewoestyne_at_pandora.be
Naamsesteenweg 328 bus 201                     GSM: +32 (0)478 397 697
B-3001 Heverlee                          http://osswin.sourceforge.net
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"Theory is the general; experiments are the soldiers." (Leonardo da Vinci)



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Octave is freely available under the terms of the GNU GPL.

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