lecturenotes10_8

lecturenotes10_8 - Newtons Method, Bisection and Function...

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Newton’s Method, Bisection and Function Handles October 8, 2008

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Topics 1. Comparing Newton’s Method with Bisection 2. Generalizing the Newton’s Method function: passing the function as an argument creating a function handle (and using it) 3. Generalizing the Bisection Function (as an example of function handles) 4. Review of Histograms
Newton’s Method vs Bisection Each of these methods has it’s own strengths and weaknesses Newton’s method will converge faster, if the slopes do not get too small near the root (or become zero) Bisection converges more slowly, but will not diverge in the process

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Example (1) Modify the bisection function that we wrote in class on Friday to solve the function f(x) = x^2 – 6x + 2. How many iterations does this take starting with xmin = 4 and xmax = 7? How many iterations did it take Newton’s Method to converge on the root with x1 = 7?
Generalizing the Solution In the previous example, we had to modify the code of the function, since the

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This note was uploaded on 02/25/2009 for the course BEE 1510 taught by Professor Staff during the Fall '05 term at Cornell University (Engineering School).

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lecturenotes10_8 - Newtons Method, Bisection and Function...

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