(4) |

Now, we choose the new interval from the two choices [*x*_{1},*x*_{3}]
or [*x*_{3},*x*_{2}] depending on in which interval
the function changes sign.

The false position method differs from the bisection method only in
the choice it makes for subdividing the interval at each iteration. It
converges faster to the root because it is an algorithm which uses appropriate
weighting of the intial end points *x*_{1} and *x*_{2}
using the information about the function, or the data of the problem. In
other words, finding *x*_{3} is a *static* procedure
in the case of the bisection method since for a given *x*_{1}
and *x*_{2}, it gives *identical* *x*_{3},
no matter what the function we wish to solve. On the other hand, the false
position method uses the information about the function to arrive at *x*_{3}.