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Fall2011-HW3

# Fall2011-HW3 - p = 4 For the Secant Method use p = 6 and p...

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Homework 3 Math 371, Fall 2011 Assigned: Thursday, September 22, 2010 Due: Thursday, September 29, 2010 Page numbers in the international edition are +12. (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 (Secant and Newton). For Newton’s Method, use
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Unformatted text preview: 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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