Convergence of Jacobi in One Dimension
For Jacobi the iteration matrix G = M-1N takes the form D-1(A-D) where D is diagonal part of A
One can calculate analytically the eigenvalues in this case and find that if one has N gridpoints, largest eigenvalue of G is
Thus if one requires an error of 10-6, then the number of iterations is given by a dreadfully large number K where