[petsc-users] Best way to compute the null space of a sparse maximum-rank rectangular matrix

Luca Argenti luca.argenti at uam.es
Sun Mar 9 12:36:43 CDT 2014

On 08 Mar 2014, at 23:11, Jose E. Roman <jroman at dsic.upv.es> wrote:

> The nullspace of A^h A is equal to the right singular space of A corresponding to the zero singular value. It should be possible to compute this with SLEPc's SVD. Computing a large number of zeros may be problematic, so I cannot say in advance if the method will succeed. If you can generate a small matrix with these properties, send it to my personal address (not the list) and I will give it a try.

Dear Jose, thank you for the answer. I thought of using the SVD (my solution would correspond to Eq. 4.4).
SLEPc guide, however, focuses on the case of a null space for A* which is much larger than its range, and 
says that the null space is often not computed at all. Furthermore, of the AA^h and A^hA cases, it says it 
takes the smallest one. In my case, that would be AA^h, and the right singular space of A would be gone at
the outset. I am glad to hear that the calculation is possible. Most probably. however, I’ll need some hints on 
how to achieve that. Finally, I really appreciate your offer of testing the algorithm; I will try to prepare a test case.



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