Question

4. The illustrative examples should show you that the simple fixed point iterations can be very slow, An alternative algorithm can be derived by using Newton's method. Suppose that A is symmetric and show that if A is equilibrated by D(x) thern Show that ef = D(x)A + D(Ax). and hence derive a Newton method for solving the symmetric equilibration problem and write a MATLAB function to carry it out. It should have the same input and output variables as your fixed point iteration in part 2. Compare its performance to the fixed point iteration on the matrices tested in part 3. Illustrate your son with appropriate graphs. Comment on the pros and cons of the Newton method, with particular reference to computational costs and suggest how these costs may be mitigated. Compare this to the power method which is hased on the stepxAx See page 12 of the fist set of notes for another esample of linear convergence

Answer 1