Transform many SVD's of small matrices to one SVD of a big matrix - possible ?

06/07/2010 - 15:49 von HannesF | Report spam
I have to solve many (~1000) independent Singular Value Decompositions
of small matrices (each is 8 x 9). Is it possible to transform the
problem somehow (to arrange all matrices somehow), so that i have to
solve only _one_ SVD of a big matrix ?
If yes, is that computationally efficient - has the 'transformed'
problem the same computational complexity as the original one ?
The reason for this is that I have efficient routines for calculating
the SVD of big matrices which I would like to use.
Any help for this issue is appreciated.
 

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#1 Alois Steindl
06/07/2010 - 16:02 | Warnen spam
HannesF writes:

I have to solve many (~1000) independent Singular Value Decompositions
of small matrices (each is 8 x 9). Is it possible to transform the
problem somehow (to arrange all matrices somehow), so that i have to
solve only _one_ SVD of a big matrix ?
If yes, is that computationally efficient - has the 'transformed'
problem the same computational complexity as the original one ?
The reason for this is that I have efficient routines for calculating
the SVD of big matrices which I would like to use.
Any help for this issue is appreciated.


Hello,
I would guess that collecting all these small matrices into a large one
would be very inefficient: The effort to do SVD scales something like
n^3 (or even worse.), so the effort to do a SVD on a matrix of order n*m
would be O(n^3 m^3), whereas for the indivial matrices your effort would
be m*O(n^3).
Also the storage requirements would increase significantly.

Usually one is quite happy if a problem can be divided into 2 distinct
parts.

Alois

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