What exactly is the Regula-Falsi Method or Method of false position in Mathematics??

The bisection method guarantees that the iterative process will converge. It is apparently slow. Thus attempts have been made to speed up the bisection method. One of them is the “Method of false position” aka “Method of Linear Interpolation”.

In this method, we choose two points x0 and x1 such that f(x0) and f(x1) are of opposite signs. Since the graph of y=f(x) crosses the X-axis b\w these two points, a root must lie in b\w these points.

f(x0)f(x1) < 0

The equation of the chord joining points {x0, f(x0)} & {x1, f(x0)} is,

So, the abscissa of a point where the chord cuts y=0, is

If f(x0) and f(x2) are new opposite signs, then the root lies b\w x0 & x. Sp. replacing x1 with x2 in the above equation, we obtain next approximation, x3. The root could also lie between x1 and x2, the find x3 accordingly. This is repeated until the root is found at desired accuracy.