 Weighted Jacobi eigenvalues for a square Dirichlet grid

For the five-point discretization of $-\Delta +c$ on the unit square, the weighted iteration eigenvalues are $1-\omega [4{\sin }^2(\pi kh/2)+4{\sin }^2(\pi lh/2)+c{h}^2]/(4+c{h}^2)$. A fixed parameter converges for every mesh when $0<\omega \le 1$, but $\omega =1$ poorly damps the highest frequencies.