I would like to understand what happens in the following:
I have a really simple Poisson problem, in 1D, with $u_0 = u_N = 0$. I assembled the stiffness matrix and the right-hand side, and I applied the BCs, then forced $A$ to be symmetric.
I'm studying the stability of an iterative method for solving this linear system while increasing $N$. I put $1e^{-10}$ as tolerance and everything went ok until $N =35000$ where around $1.2e^{-10}$ the residual starts to oscillate.
As a test I tried a solving in Matlab (using A\b
), and also there the residual did not go below $1e^{-10}$.
So I removed the symmetry from the stiffness matrix, and I retried on Matlab, and now the residual is in the order of $1e^{-11}$.
So, is it possible that a simple manipulation for making the matrix symmetric could cause my solution to be "worse"?