What Secrets the Bisection Method Hides?

[Namir]

The root-seeking Bisection method is the simplest, slowest, but very reliable algorithm for finding the root of a function. The method is know for choosing a refined guess value in the middle of the root-bracketing interval (A, B). The refined root is calculated using:

C = (A + B) / 2

The value of C replaces either A or B, based of matching function signs.

I wrote a paper (click here) that looks at the above equation in more general terms:

C = (w1 * A + w2 * B) / (w1 + w2)

The paper explores using different combinations of w1 and w2 and how most of these combinations can reduce the number of iterations needed to reach a refined guess for the root at a specific tolerance value.

Some people just won't leave "well-enough" alone :-)

Namir