m371-f10-hw3 - (Secant and Newton). For Newtons Method, use...

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Homework 3 Math 371, Fall 2010 Assigned: Thursday, September 23, 2010 Due: Thursday, September 30, 2010 Include a cover page Clearly label all plots using title , xlabel , ylabel , legend Use the subplot command to compare multiple plots Include printouts of all Matlab code, labeled with your name, date, section, etc. (1) (Rootfinding and Optimization cont.) (a) Let us continue the previous assignment for finding the unique maximum of f ( x ) = log x - sin x in the interval [4 , 6]. (Note that log means natural logarithm.) Previously, you approximated the local maximum using six iterations of the Bisection method. (b) Approximate this local maximum using six iterations of the two fixed-point methods
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Unformatted text preview: (Secant and Newton). For Newtons Method, use p = 4. For the Secant Method, use p = 6 and p 1 = 4. (c) What is your best estimate for p , the location of the maximum? (d) Compare the three algorithms using the following two tables. Table 1: Approximation p n versus iteration number n Iteration n Bisection Secant Newton Table 2: Absolute error | p n-p | versus iteration number n Iteration n Bisection Secant Newton (e) What happens if you attempt to approximate the maximum by starting Newtons Method with p = 6? (2) (Newton versus Secant) Bradie, p. 113, #12. 1...
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This note was uploaded on 09/28/2010 for the course MATH 371 taught by Professor Krasny during the Fall '08 term at University of Michigan.

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