[petsc-users] Yet another inversion question

[Jed Brown]

On Sat, 01 May 2010 22:27:15 +0200, Umut Tabak <u.tabak at tudelft.nl> wrote:
> Dear all,
> 
> I need some terms in my algorithm such as
> 
> A^{-1} B

You say that both A and B are sparse, what are you going to do with the
product C = A^{-1} B?  The most common thing is to apply it to some
vectors or perhaps compute a few eigen/singular values/vectors.  You
rarely need an explicit representation of the product to do such things.

> so what would be the best way to compute this dense symmetric
> resulting matrix.

It is extremely unlikely that C is symmetric.

> I did a  first try to  solve for the columns of B, with the umfpack 
> interface and direct solve

This will work, you could also use the lower level interface to factor
A, MatConvert() B to MATDENSE, then MatMatSolve() the result.
Internally this will do something very similar to what you have already
done, it's questionable whether it would actually be faster (it will
certainly use more memory).

Jed