# Regular Falsi Method

**Regular Falsi Method:**

This method is also called as false position method. Consider the equation Bisection Method. Let a and b, such that a < b, be two values of x such that f (a) and f (b) are of opposite signs. Then the graph of y = f (x) crosses the x-axis at some point between a and b.

The equation of the chord joining the two point (a, f (a)) and (b, f (b)) is,

Now if function is considered as a straight line, the intersection of chord produces as approximate root value. Further very similar to Bisection Method root lies in between a and x_{1} or between x_{1} and b, depends upon the fact f (a) f (x_{1}) < 0 or f (x_{1}) f (b) < 0 respectively. Thus we may concentrate on smaller interval in which root lies. We repeat this process with interval in which root lies. Suppose that we are given an interval [a,b] satisfying Bisection Method and an error tolerance ε > 0. Then the Regula Falsi Method is consists of the following steps:

**Figure of Regular Falsi Method:
**

**R1**. Compute c

**R2**. If the difference with two consecutive c is less than or equal to ε, then accept c as the root and stop the procedure.

**R3.** If f (a). f (c) ≤ 0, then set b = c else, set a = c. Go to step B1.