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CMPSC 200: Assignment 3 Due Date: May 1 in class (last day of class) Rules: Submit a copy of your report and hardcopies of each algorithm and as well as the corresponding gures. Please cite any reference that you used in you report. The assignment will be graded out of 100 points representing 15% of your total score. Late submissions will not be accepted. Remember to put in names of all the members of the group in your submission. One sub- mission per group is sucient. Objective: Solve nonlinear functions. 1. Using the Inv.m and Newton.m les from the sample code, solve the following nonlinear equations and obtain corresponding fractals, based on the value of the roots. Use symbolic mathematics to obtain the roots initially so that you can color code them.(5X7=35). (a) (z2 + 4)(z2 􀀀 4) (b) z3 􀀀 1 (c) z3 + 1 (d) z4 􀀀 1 (e) z4 + 1 2. Modify the last part of Newton.m function, such that W stores the number of iterations required to nd the root. Plot this W using Inv.m for any two of the above equations. (20+10=30). 3. Compare the time taken by the Bisection method and the Newton method. To do this x a and b for the bisection method and the initial value of z for the Newton method and solve a nonlinear equation. For example for the nonlinear equation (z2 + 4)(z2 􀀀 4), set a = 0 and b = 8 for the Bisection Method and z = 0 for the Newton Method. Set tol = :0001 and maximum iterations to 40. (20) 4. Write a report including the following points. (15) (a) A short description of Newton's method. 5 (b) Name an algorithm f(other than Newton and Bisection) for solving nonlinear equations. Why are nonlinear functions more dicult to solve than linear ones ? 5 (c) What was the most interesting part about this project and what was the most dicult part 5 1