invert nearly singular matrix

I am trying to solve the poisson equation in cylindrical coordinates using a finite difference which essentially narrows down to Ax = B where A is a finite difference matrix, x and B are column vectors. I am solving for x and unfortunately A is nearly singular. So when I do x = A\B i get inaccurate answers. Is there a way to accurately solve this issue?

Answer 1

[Jan]

Some instable systems caused by nearly singular matrices can be solved sufficiently using quadrupel precision. See INTLAB of Rump, http://www.ti3.tu-harburg.de/rump/Research/topics.php.