# [petsc-users] linear system solution for slightly changing operator matrix

Umut Tabak u.tabak at tudelft.nl
Tue Feb 16 03:13:17 CST 2010

```Dear all,

My question is not directly related to PETSc usage, however since I use
PETSc to test my ideas. I wanted to ask here.

I believe there are many numerical experts in this group from whom I can
get some advice on linear system solutions. In brief, I was working on
an iterative correction algorithm for coupled vibroacoustics in the last
months, at each iteration I have to update an operator matrix and rhs
vectors and solve this system for corrections, x.

More specifically the system is(there are two systems like this but they
are built on the same idea: to solve linear systems for correction
vectors, x)

(A - y * B) x = y * C * v

where y and v are the eigenvalues and eigenvectors coming from an
eigenvalue problem,respectively, and updated at each iteration to end up
with new correction vectors x(and say x' for the other linear system).
A, B are sparse symmetric matrices, C is not symmetric but pretty sparse.

I try to solve these systems  iteratively, by cg in PETSc with the some
preconditioners, for the moment icc gave the best results for my problem.

However, I realized that the  eigenvalues which  affect the build  up of
the operator matrix,(A - y * B), namely y values, do not change too much
from one iteration to another(Of course after 1 or 2 iterations, they
start oscillating around more or less the same values that is what I
call they do not change too much). The question is that can this little
change(s) be handy to be able to use some information from the previous
linear system solutions? If yes, how should I advance to make these
linear solves faster?

Any directions/pointers are appreciated.

Best regards,

Umut
```