This method is also called interval halving method and is used to find root of an equation in a given interval ( finding value of x for which f(x)=0 )
It uses a linear interpolation to find an approximation of yhe root . It calculates the root of the line segment connecting f(a) and f(b) which tends to be closer to the actual root than midpoint used in bisection method

Advantages of this method
Fast converging than bisection method for functions that are approximately linear in [a,b]
It uses the function's values to get a better estimation of the root

Disadvantages of this method
If the f isn't approximately linear in [a,b] the convergeance will be slow
Can stuck if subinterval is repeatedly chosen without significant improvement