Weighted Jacobi eigenvalues for a square Dirichlet grid
= Weighted Jacobi eigenvalues for a square Dirichlet grid
{title2=$\lambda_{k,l}(H_\omega)$}
For the five-point discretization of $-\Delta+c$ on the unit square, the weighted iteration <eigenvalues> are $1-\omega[4\sin^2(\pi kh/2)+4\sin^2(\pi lh/2)+ch^2]/(4+ch^2)$. A fixed parameter converges for every mesh when $0<\omega\leq1$, but $\omega=1$ poorly damps the highest frequencies.