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m371-f10-hw3

# m371-f10-hw3 - (Secant and Newton For Newton’s 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 Newton’s 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 Newton’s Method with p = 6? (2) (Newton versus Secant) Bradie, p. 113, #12. 1...
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