a) Show that Jacobi’s method for solving \(Ax=b\) iteratively is convergent when \(A\) is strictly diagonally dominant. What does this imply about the spectral radius of another matrix obtained from \(A\).
b) Describe the successive over-relaxation (SOR) method with parameter \(\omega \) and it’s rate of convergence. Give a sufficient condition upon \(A\) and \(\omega \) for convergence.
c) Briefly compare the complexity of solving Poisson’s problem in three dimensions by direct and iterative methods. Assume the simplest methods, grid, differencing scheme, boundary conditions, etc.