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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 9, 2010 9:55 AM
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On 9 Giu, 15:15, Brian Borchers <borchers.br...@gmail.com> wrote:
> On Jun 9, 5:40 am, luca <luca.frammol...@gmail.com> wrote:
>
>
>
>
>

> > Hi,
>
> > i have fear of asking this question, because it could be stupid, but i
> > will try it nevertheless:

>
> > suppose i have a matrix A N x 8, where N is of order 10^3-10^5 and a
> > vector v of size Nx1 (all are real elements).

>
> > To compute the element (i, j) of A i need to do some computation
> > (derivative of image pixels, some multiplications and so on). After
> > computing A, i need to compute its pseudo-inverse: pinvA = (A^T *
> > A)^-1 * A^T (where A^T is the transpose of A and (..)^-1 is the
> > inversione of the quantity between parenthesis)  and finally i need to
> > compute the multiplication of the pesudoinverse by v:

>
> > pInvA * v
>
> have you considered using the singular value decomposition to find the
> pseudoinverse of A?  This would save you the trouble of multiplying
> out A'*A and avoid the ill-conditioning of the A'*A matrix.
>
> Yes, 1.0e11 is a big condition number- you want to avoid working with
> A'*A if possible.- Nascondi testo citato
>
> - Mostra testo citato -


Hi,
mmm, don't know, the SVD of A should be too heavy from a computational
point of view (i am writing a real-time application)...



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