Editing Root-finding algorithm (section)

=== False position (''regula falsi'') ===
The [[false position method]], also called the ''regula falsi'' method, is similar to the bisection method, but instead of using bisection search's middle of the interval it uses the [[x-intercept|{{math|''x''}}-intercept]] of the line that connects the plotted function values at the endpoints of the interval, that is 
:<math>c= \frac{af(b)-bf(a)}{f(b)-f(a)}.</math>

False position is similar to the [[secant method]], except that, instead of retaining the last two points, it makes sure to keep one point on either side of the root. The false position method can be faster than the bisection method and will never diverge like the secant method. However, it may fail to converge in some naive implementations due to roundoff errors that may lead to a wrong sign for {{math|''f''(''c'')}}. Typically, this may occur if the [[derivative]] of {{mvar|f}} is large in the neighborhood of the root.