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Wednesday, February 11, 2015

Root finding algorithm without using derivatives

This algorithm finds a root of an equation, like Newton's method, but is designed for situations when the function in question can be solved for x from a function f(x) though the derivative might be complicated or expensive to calculate making many other algorithms like Newton's method unsuitable...
Starting with an example function:
One first solves the equation for one x on the left from the original equation:
Then set y = 0 in this equation...
Then use this above formula and plug into a recursive structure like this:
Now you can plug in an initial guess (here -2):
And proceed recursively...
It approaches the root of 1.6666 quadratically...

**Proof**
Still working on a good proof...


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