
Ublas : 
From: Karl Meerbergen (Karl.Meerbergen_at_[hidden])
Date: 20070213 11:32:26
Gunter Winkler wrote:
>Am Dienstag, 13. Februar 2007 00:28 schrieb
>Richard_Harding_at_[hidden]:
>
>
>>Hello,
>>
>>I have a very sparse matrix (<= 6 nnz entries per row with
>>potentially thousands of columns) which I need to premultiply by its
>>transpose in order to solve the normal equations associated with a
>>leastsquares computation: (A'A)x = A'b. I may have missed them, but
>>
>>
>
>Don't do this  trust me ;)
>
>in order to solve the least squares problem you do a QRdecomposition of
>A and get the cholesky decomposition of A'A for free:
>
>A = QR > A'A = (QR)'QR = R'Q'QR= R'R
>
>
True. But you need a sparse QR factorization. It exists, but I do not
recall precisely where you can find code. A sparse QR can be done with a
sparse GramSchmidt routine. Needless to say that fillin is going to
grow. Developing an efficient code using BLAS 3 etc is quite a job.
Karl
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