Derivation of The Method
Starting with initial values and, we construct a line through the points and, as demonstrated in the picture on the right. In point-slope form, this line has the equation
We find the root of this line – the value of such that – by solving the following equation for :
The solution is
We then use this new value of as and repeat the process using and instead of and . We continue this process, solving for, etc., until we reach a sufficiently high level of precision (a sufficiently small difference between and ).
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Read more about this topic: Secant Method
Famous quotes containing the word method:
“You know, I have a method all my own. If you’ll notice, the coat came first, then the tie, then the shirt. Now, according to Hoyle, after that the pants should be next. There’s where I’m different. I go for the shoes next. First the right, then the left. After that, it’s every man for himself.”
—Robert Riskin (1897–1955)