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MAKE A MEME View Large Image $Newtons method failure.png en Graph showing a case where Newton's method fails to converge on a root Newton's method applied to the function<br/><math>f\left x\right \begin cases \sqrt x-4 \mbox for \ \ x \ge 4 \\ -\sqrt 4-x \mbox for \ \ x ...$

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Keywords: Newtons method failure.png en Graph showing a case where Newton's method fails to converge on a root Newton's method applied to the function<br/><math>f\left x\right \begin cases \sqrt x-4 \mbox for \ \ x \ge 4 \\ -\sqrt 4-x \mbox for \ \ x < 4 \end cases </math><br/>starting with <math>x_0 2</math> For this function choosing any <math>x_1 r - h</math> then <math>x_2 r + h</math> would cause successive approximations to alternate back and forth so no amount of iteration would get us any closer to the root than our first guess Function has inflection point method has a cycle and never converge My own work Paul Breen 2011-05-01 Cc-zero Newton Method