Using MATLAB or FreeMat

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The equation 2x3 + 3x + 5 cos esin 2 = 1 + x2 has three solutions. The goal of this project is to use Fixed Point Iteration to find all three solutions and analyze the linear convergence rate of FPI to the roots. 1. Use the Fixed Point Iteration method to calculate all three roots, each rounded to 10 correct decimal places. Each root r will be a fixed point of FPI with a particular g(x). You may find it necessary to use more than one g(x) to find them all, and you may need to vary the initial guesses as well. For each root of the equation, report the fixed point rounded accurately to 10 decimal places, the g(x) and initial guess you used, and the number of FPI steps required to reach this accuracy. 2. For each fixed point r, use calculus to determine S = \g'(r)]. 3. For each fixed point r, use your Matlab calculations to approximate the convergence rate lime;+1 ito ei of the Fixed Point Iteration. Our theory says that this limiting ratio should be S. Show that your approximate limits match with the answers in part 2. The equation 2x3 + 3x + 5 cos esin 2 = 1 + x2 has three solutions. The goal of this project is to use Fixed Point Iteration to find all three solutions and analyze the linear convergence rate of FPI to the roots. 1. Use the Fixed Point Iteration method to calculate all three roots, each rounded to 10 correct decimal places. Each root r will be a fixed point of FPI with a particular g(x). You may find it necessary to use more than one g(x) to find them all, and you may need to vary the initial guesses as well. For each root of the equation, report the fixed point rounded accurately to 10 decimal places, the g(x) and initial guess you used, and the number of FPI steps required to reach this accuracy. 2. For each fixed point r, use calculus to determine S = \g'(r)]. 3. For each fixed point r, use your Matlab calculations to approximate the convergence rate lime;+1 ito ei of the Fixed Point Iteration. Our theory says that this limiting ratio should be S. Show that your approximate limits match with the answers in part 2