Consider the linear system Au = b, where

(a) What is the solution?
(b) Discuss the convergence of the Jacobi iteration method.
(c) Discuss the convergence of the Gauss-Seidel iteration method.
(d) Write down the explicit formulas for the SOR method.
(e) What is the optimal value of the relaxation parameter co for this system? How much faster is the convergence as compared to the Jacobi and Gauss-Seidel methods?
(f) Suppose your initial guess is u(0) = 0. Give an estimate as to how many steps each iterative method (Jacobi, Gauss-Seidel, SOR) would require in order to approximate the solution to the system to within 5 decimal places.
(g) Verify your answer by direct computation.

Transcribed Image Text:

2 3 1