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9.3 An Alternative: the Halving Method

This is an alternate method for solving equations, which, if it can be started, always produces a solution between the initial starting points.  


To solve equation f(x)=0.

To start you must find two points, a and b, such that f is positive at one and negative at the other.

Suppose f(a)>0 and f(b)<0.


Examine .

If it positive replace b by .

Repeat this step until the resulting a and b are indistinguisable to the accuracy you desire.

The resulting a or b is your solution.

Notice that the distance between a and b after n steps is |b - a|2-n.