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Topic: Matrix multiplication by its transpose
Replies: 11   Last Post: Jun 13, 2010 11:04 AM

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luca

Posts: 11
Registered: 5/19/10
Re: Matrix multiplication by its transpose
Posted: Jun 10, 2010 5:15 AM
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On 10 Giu, 07:15, aruzinsky <aruzin...@general-cathexis.com> wrote:
> On Jun 9, 9:30 am, aruzinsky <aruzin...@general-cathexis.com> wrote:
>
>
>

> > ...
> > **** OR ****

>
> > Possibly in single precision to save time, use row sequential Givens
> > rotations to form factors R and QTv1 on fly (This is QR decomposition
> > but Q is not explicitly calculated).   Note, v1 needs to be calculated
> > on a separate preliminary pass. Then solve

>
> > R x1 = QT v1
>
> > by back substitution.
>
> > In either case, check that ATA is not singular by examining the
> > diagonal of R for zero elements.  Or, put small fictional data into A
> > to prevent the possibility of singularity.- Hide quoted text -

>
> -
>
> That's wrong.  In the Givens method, ATv is not calculated.  The
> method gives R and QTv by sequentially processing rows ai and elements
> vi, and then you solve
>
> R x1 = QT v
>
> by back substitution.  I can't find a reference on the web to explain
> the details but, if interested, I can give you C++ code.- Nascondi testo citato
>
> - Mostra testo citato -


Wow, thank you very much! Are you aware of a good text where i can
find infos
that allow me to speed up computation (like the method you pointed to
me on how to compute ATA on the fly)?

However, send me the source code. I am interested in the faster way to
do this...

A question: is Cholesky decomposition affected by the ill-conditioing
of the matrix ATA?

Thank you again,
Luca



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