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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Famous quotes containing the word method:
“Protestantism has the method of Jesus with His secret too much left out of mind; Catholicism has His secret with His method too much left out of mind; neither has His unerring balance, His intuition, His sweet reasonableness. But both have hold of a great truth, and get from it a great power.”
—Matthew Arnold (1822–1888)