Efficient LSV Approximation for Large Matrices | Conjugate Gradient Method Guide

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For certain computations I need a quick approximation of the left singular vector of a matrix G( nxk ; n>k ). Also, the corresponding singular value would be needed. Perhaps after approximating the singular value I could use the Conjugate Gradient method to obtain the approximation of the left singular vector. Any idea on how to achieve this would be very welcome.
Note that for matrix G, n which is the number of rows, is very large ( n>>k).
Thanks
 
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I read that Truncated SVD might be one of the solution for my problem:
http://en.wikipedia.org/wiki/Singular_value_decomposition#Truncated_SVD
Unfortunately, there are no examples I might use in order to implement this method.
Note that there is a need for Left singular vector (if it is not necessary to compute the Right singular vector) only
and the largest singular value (to be precise I need 2 LSVectors and the corresponding largest 2 singular values).
Any other suggestion on how to achieve this, or an example on how to perform Truncated SVD is very welcome.
 
Anyone?
 

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