hw4 - Assignment#4 Root Finding(contd Polynomial...

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Assignment #4: Root Finding (cont’d), Polynomial Interpolation Due date: Monday, October 11, 2010 (10:10am) For full credit you must show all of your work. 1. Illustrate each of the possible outcomes listed below, by giving an example of a function and an initial estimate that will cause Newton’s method to: a. diverge to positive or negative infinity b. cycle endlessly without ever converging c. fail because of an attempt to divide by zero d. cycle for a while and then converge e. converge steadily but very slowly f. converge quickly [Hint: you can get some ideas from examples given in class and from the problems at the end of chapter 3] 2. By hand, estimate a root of f ( x ) = x 3 ½ x + 1 by using two iterations of the Secant Method, with x 0 = 0 and x 1 = 1. Repeat using x 0 = 1 and x 1 = 0. 3. Using Matlab, write a general purpose function Secant that uses the Secant Method to locate a root of a pre-defined function f , given two initial starting points x 0 and x 1 . [Let f be defined independently from Secant , and let x 0 and x 1 be parameters that are input by the user.] Use good programming practices to ensure that the program terminates
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hw4 - Assignment#4 Root Finding(contd Polynomial...

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