singular matrix

[Jose E. Roman]

On 16/04/2009, Yixun Liu wrote:

> Hi,
> For Ax=b, A is mxn, m>n. I use CG to resolve it and find the solution
> makes no sense.  I guess rank(A) < min(m,n). How to resolve this
> singular system? Use SVD?
>
> Best,
>
> Yixun

Although it is probably not the most efficient way, you can use SLEPc  
to compute an SVD-based approximation of the pseudo-inverse, A+, then  
pre-multiply vector b. The following sequence should do the task.

1) Compute p<n singular triplets with SLEPc's SVD solver.
2) VecMDot of b with the left singular vectors.
3) Scale the resulting values with the reciprocals of singular values.
4) VecMAXPY of right singular vectors using the coefficients obtained  
in 3)

Jose