My problem is that the L2-Norm of the residual for the periodic Poisson matrix $P$ is initially decreasing but starts to blow up after a certain number of iterations. The blowup happens earlier the larger the matrix is.
On the other hand, the Poisson matrix $H$ with homogeneous Dirichlet boundary condition converges exponentially for many iterations without any notable oscillations.
For reference, I am using the CG algorithm presented here from Wikipedia.
The only criterion for convergence I came across seems to be the positive definiteness of the system matrix. What could possibly lead to the blowup with matrix $P$?