3. (Fized-Point Iteration). Consider the problem of finding the root of the polynomial f(x)=-0.912-1.07 in [1,2]. (1) Show that -0.91-1.07-01= $0.91z+1.07 on [1,2]. Execute the commands plot yn (0.91 x 1.07)-(1/4) and ye1 and y2 for 1.. 2 plot y 0 (0.91 x 1.07)-(1/4) ) and ye-1 and ye1 for x= 1. 2 at the Wolfram Alpha (Wa) website to demonstrate, as we did during the lectures, that the iteration function 9(z) = 0.91z+1.07 satisfies the conditions of the main statement on convergence of the Fixed-Point Iteration method from the lecture notes on the interval [1,2]. Copy (with your own hand) both graphs in your work. Based on the graphs, make a conclusion on convergence of the FPI for the problem at hand. (H) Use the Fixed-Point Iteration method to find an approximation py of the fixed-point p of g(x) in (1.2), the root of the polynomial f(z) in [1,2], satisfying RE(PNPN-1) < 10-7 by taking po=1 as the initial approximation. All calculations are to be carried out in the FFA,. Present the results of your calculations in a standard output table for the method of the form Pn-1|P|RE(ps P-1) (Your answers to the problem should consist of two graphs, a conclusion on convergence of the FPI, a standard output table, and a conclusion regarding an approximation px.)
