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Unformatted text preview: ME 218: ENGR COMPUTATIONAL METHODS
Lecture Notes (Set #4) Secant Method
To overcome the need in the Newton-Raphson 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 Newton-Raphson’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) ⎠ྏ
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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