Consider the nonlinear equation f(x) = x3?2x2 ? x + 2 = 0.
(a) Verify that x = 1 is a solution.
(b) Convert f(x) = 0 to a fixed point equation g(x) = x wherethis is not the fixed point iteration implied by Newton’s method,and verify that x = 1 is a fixed point of g(x) = x.
(c) Convert f(x) = 0 to the fixed point iteration implied byNewton’s method and again verify that x = 1 is a fixed point.
(d) Write MATLAB code to iterate on your fixed point iterationas well as the fixed point iteration implied by Newton. Comparethese results based on x0 = 1.1. How fast did Newton converge? Howfast did your iteration from part b converge (or did it at all)?What does the theory of fixed points tell you about theseconvergence results?
