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Unformatted text preview: ME 218: ENGR COMPUTATIONAL METHODS
Lecture Notes (Set #4) Secant Method
To overcome the need in the NewtonRaphson iterative scheme to evaluate first
derivative of the function, or the possibility of the derivative going to zero, the Secant
Method can be used. It utilizes the information of a second point to evaluate the
derivative, by assuming that the function is linear in the domain of interest.
From the NewtonRaphson’s method:
x2 = x0 – f(x0)/f’(x0)
But using another point, x1, between x2 and x0 to determine the derivative, f’(x0):
f’(x0) = (f(x1) – f(x0))/(x1 – x0)
Thus, generalizing the iterative scheme: ⎛ྎ x N − x N −1 ⎞ྏ
x N +1 = x N − f(x N )⎜ྎ
⎟ྏ
⎝ྎ f(x N ) − f(x N −1) ⎠ྏ
The computation...
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This note was uploaded on 12/14/2011 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas at Austin.
 Fall '08
 Unknown

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