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Unformatted text preview: Due: October 16, 2008 CS 257 (Luke Olson): Homework #6 Problem 1 Problem 1 You are writing an API for a finance company which is in need of a solver for finding the roots of nonlinear equations (i.e. finding an x such that f ( x ) = 0). You decide to implement Newton’s method in MATLAB. (Newton’s method is given in Lecture 13.) The function takes as arguments f,f ,x ,maxiter where f is the function we want to find the zeros of, f its derivative, x the initial guess and maxiter is the maximum number of iterations. For each iteration, output the following table. Iteration number x i f ( x i ) f ( x i ) /f ( x i- 1 ) 2 f ( x i ) /f ( x i- 1 ) Run your program on the following test cases a. f ( x ) = e- x- cos( x ), x = π/ 2, maxiter = 10 b. f ( x ) = 2 x 3- 9 x 2 + 12 x + 15, x = [2 . 99 , 3 , 3 . 01], maxiter = [20 , 4 , 20] c. f ( x ) = p | x | ,x = 0 . 5 ,maxiter = 10 hint: f ( x ) = sign ( x ) 2 √ | x | and for each case, determine if the method converges. If so, is the convergence quadratic or linear? If is not quadratic explain why.quadratic explain why....
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This note was uploaded on 07/10/2011 for the course CS 257 taught by Professor Olson during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08