ME 218 Fall 2010 HW 3 Solutions

ME 218 Fall 2010 HW 3 Solutions - ME 218 Fall 2010 HW 3...

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Unformatted text preview: ME 218 Fall 2010 HW 3 Solutions Problem 1 Given the function () ( () ) we are asked to perform 3 iterations of the secant method in order to find a root. Here I will demonstrate the first step, with the given initial points. () () () () ( ( )) Now we employ the secant method () () ( ( ( )( ( ( ( ) ) ) ( () ) ) ) ) ( ) Here is the Excel-generated table to complete the iterations n Then, x_(n-1) x_n f(x_(n-1)) f(x_n) x_(n+1) 1 0.0000 0.5000 -1.0210 0.0204 0.4902 2 0.5000 0.4902 0.0204 0.0101 0.4805 3 0.4902 0.4805 0.0101 -0.0004 0.4809 ,() , and the last iteration step made is of length | | Following are a numerical result and graphical representation of the solution generated by MATLAB. . 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 f(x) g(x) = 0 -0.6 -0.7 -0.8 0 0.1 0.2 0.3 0.4 0.5 x 0.6 0.7 0.8 0.9 1 Problem 2 a) ( ) b) Trivial c) ( ( ( ( ) ) ( ) ) ( ) ) ( ) In this problem, it is important that students notice that the multiplications systematically reduce A to the identity matrix. ...
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This note was uploaded on 09/05/2011 for the course ME 205 taught by Professor Koen during the Spring '07 term at University of Texas.

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