Hello everyone,

I have a question regarding the sparse matrix solver which I have

discussed with a friend of mine.

AX=0 (an eigenvalue problem)

where, the matrix A is from the standard five-points finite-difference

discretization. It is sparse banded matrix with only five non-zero

each row. It is looks like:

1/dy/dy……..1/dx/dx -2/dx/dx-2/dy/dy+K 1/dx/dx……..1/dy/dy

where dx, dy are the mesh size in X- and Y-dimension.

In the discussion, if the parameter K<0 (valid for most grids),

then A matrix is diagonal dominant, and the sparse matrix solver,

such ORTHOMIN, BI-CG, or BI-CGstab may be used.

The problem is, at some grids, the K>0, which destroys the diagonal

dominance. In this case, will the sparse matrix solver converge ?

BTW, the preconditioner used is DKR factorization.

Thanks in for any suggestion.

Fred