Secant Method - Derivation of The Method

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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