446proj2

# 446proj2 - this accuracy 2 For each ﬁxed point r use...

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MATH 446 / OR 481 SAUER SPRING 2010 Project 2 Finding Roots by Fixed Point Iteration Use Fixed Point Iteration to ﬁnd all roots of the equation 3 x 3 - 7 x 2 + 3 x - e x + 2 = 0 , and analyze the linear convergence rate of FPI to the roots as follows. 1. Use Fixed Point Iteration to calculate all roots, rounded to 8 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 accurate to eight decimal places, along with the g ( x ) and initial guess you used, and the number of FPI steps required to reach
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Unformatted text preview: 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 lim i →∞ e i +1 e i of the Fixed Point Iteration, and match your approximations with the an-swers in part 2. One extra bonus point will be awarded to the student who ﬁnds the fastest convergence to a root, as measured by the smallest nonzero S . Begin your report by answering the three questions above. Print out the Matlab code used and your Matlab session, and include these with your report. Due: Thurs., Feb. 4...
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