Math 481a, Spring 2005 Project 1. The root finding problem Summary: Math 481a, Spring 2005 Project 1. The root finding problem Due MARCH 28, 2005 Problem 1: Compare performance of three root-finding algorithms: Newton's method, bisection method, and the fixed-point iteration method. · Write a code implementing Newton's method, bisection method, and the fixed-point method. Keep the programing in such a way as to be able to compare performance of the three methods on a selected function. · For each method, by experiments and from theoretical facts, construct an example of function (3 examples in total) such that the root finding problem is best solved with that method. Explain, how you construct your examples. · Write a report. Include results of your calculations with some minor comments, and justify the choice of examples. Attach the code. Problem 2: Compare performance of Newton's method and Muller's method on the problem of finding roots of a polynomial with real co- efficients by the method of deflation. · Write a code implementing deflation method for finding all roots Collections: Physics