Lecture 3 Typeset Notes

x x0 f x0 rearranging x x0 fx0fx0 where

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Unformatted text preview: series expansion, f ( x) $ 0 $ f ( x0 ) ! ( x # x0 ) f "( x0 ) Rearranging, x = x0 – f(x0)/f’(x0), where x0 is the initial guess. Generalizing the iterative process: xN+1 = xN – f(xN)/f’(xN), till |xN+1 – xN| < e This method converges faster than the Bisection and the Regula-Falsi methods, but suffers from the drawback that the process might hit a local extremum and make the derivative term go to zero. In that case, the method becomes unstable, as there is a division by 0! 1 Secant Method To overcome the need in the Newton- Raphson iterative scheme to evaluate first derivative of the...
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This note was uploaded on 10/03/2012 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas at Austin.

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