446proj3 - i from the Newton iteration and compare with the theoretical answer 4 For each root for which Newton’s Method converges linearly

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MATH 446 / OR 481 SAUER SPRING 2010 Project 3 Convergence of Newton’s Method The equation 27 x 4 - 54 x 3 - 72 x 2 - 26 x - 3 = 0 . has two roots. 1. Plot the function f ( x ) for - 4 < x < 4 , - 100 < y < 100 to get an idea where the roots are. 2. Use Newton’s Method to calculate both roots to as many correct decimal places as you can. For each root, underline or boldface the digits you believe to be accurate. Is there a difference, between the two roots, in accuracy (forward error) that Newton’s Method can achieve? Explain why there is a difference. 3. For each root for which Newton’s Method converges quadratically, calculate the ratio lim i →∞ e i +1 e 2
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Unformatted text preview: i from the Newton iteration and compare with the theoretical answer. 4. For each root for which Newton’s Method converges linearly, calculate the ratio lim i →∞ e i +1 e i from the Newton iteration and deduce the multiplicity of the root. 5. For each root above, find the interval [ a,b ] of initial guesses for which New-ton’s Method converges to that root. Begin your report by answering the questions 2 – 5 above (include your plot somewhere). Print out the Matlab code used and your Matlab session, and include these with your report. Due: Thurs., Feb. 11...
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This note was uploaded on 10/27/2010 for the course MATH 446 taught by Professor Staff during the Spring '08 term at George Mason.

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