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From: Oleg Komarov on 11 Jan 2010 07:40
"John D'Errico"
> If it is a question of wanting to program the QR
> itself, then it really is time to return to the books,
> as we will not write that code for him, even though
> it is not that difficult to write.
>
> John
John,
I don't have a really strong maths background. Can you suggest any good math reference on matrix factorization where the subject is explained in a step by step approach (possibly with examples)?

I have read something on Cleve's book (see above). I find it quite useful but I can't tell if something more detailed and simpler exists...

Thanks

Oleg
From: John D'Errico on 11 Jan 2010 09:44
"Oleg Komarov" <oleg.komarov(a)hotmail.it> wrote in message <hif67k$e52$1(a)fred.mathworks.com>...
> "John D'Errico"
> > If it is a question of wanting to program the QR
> > itself, then it really is time to return to the books,
> > as we will not write that code for him, even though
> > it is not that difficult to write.
> >
> > John
> John,
> I don't have a really strong maths background. Can you suggest any good math reference on matrix factorization where the subject is explained in a step by step approach (possibly with examples)?
>
> I have read something on Cleve's book (see above). I find it quite useful but I can't tell if something more detailed and simpler exists...
>

I'm not sure what you are looking for. This seems to
give a reasonable explanation of what is necessary, but
I have the feeling that you want more.

http://en.wikipedia.org/wiki/Householder_transformation

A QR is simply a sequence of householder transformations,
used to generate an upper triangular result.

So I would suggest that you write a function that forms
and applies ONE householder transformation to a matrix.
Then just call it in a loop. As you kill off what is in one
column of A, you build up Q at the same time, starting
from an identity matrix. When A is finally upper triangular,
then Q is done too.

John
From: Oleg Komarov on 11 Jan 2010 10:53
John D'Errico,
> I'm not sure what you are looking for. This seems to
> give a reasonable explanation of what is necessary, but
> I have the feeling that you want more.

Yes, i want more :).
I already read the wiki page but I feel a little confused.
I was looking for something that explains linear systems with a more general approach (like Cleve's book but with stronger mathematical background, but maybe better reference is hard to find if not to attend a course in mathematics).
Any advice on a good textbook that starts from a to z (as we say in Italy) will be appreciated.

Thanks
Oleg
From: Marko Mijatovic on 12 Jan 2010 14:55
"Oleg Komarov" <oleg.komarov(a)hotmail.it> wrote in message <hifhh0$4uu$1(a)fred.mathworks.com>...
> John D'Errico,
> > I'm not sure what you are looking for. This seems to
> > give a reasonable explanation of what is necessary, but
> > I have the feeling that you want more.
>
> Yes, i want more :).
> I already read the wiki page but I feel a little confused.
> I was looking for something that explains linear systems with a more general approach (like Cleve's book but with stronger mathematical background, but maybe better reference is hard to find if not to attend a course in mathematics).
> Any advice on a good textbook that starts from a to z (as we say in Italy) will be appreciated.
>
> Thanks
> Oleg

from regular quadratic matrix A to calculate A ^ -1 so as to solve AX = I so that n times apply solution with the help of QR-factorization (ie Ax1 = e1, x1 first column of the matrix X )..... QR faktorization is needed only once
From: Pat Finder on 13 Jan 2010 01:01
"Oleg Komarov" <oleg.komarov(a)hotmail.it> wrote in message <hieted$40j$1(a)fred.mathworks.com>...
> "Matt J "
> > > I cant just type inv qr(A)!!!
> >
> > To quote your original post, you said you were "just missing matlab code with QR factorization..."
> >
> > This makes it sounds like the problem you were having is that you did not know how to obtain the QR factorization using MATLAB.
> >
> > Since the qr() function does this, and if you understand that, it is not clear what further help you were hoping to get from us...
>
> I think he wants to know how, in specific, is achieved the QR decomposition. Since in MATLAB it's a builtin fcn, the code isn't available.
> I suggest to look for 'householder reflection' in wikipedia and 'Numerical Computing' by Cleve Moler (MATLAB chief scientist): http://www.mathworks.com/moler/
>
> Oleg
I recommend you buy Cleve's book. It is great. There is a new revision, and he discusses the importance of the Householder transform.
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