Linear Interpolation Method

The linear interpolation method is a kind of bracketing methods. Like the bisection method, this method finds the approximated position of root through a specified interval. In this method the root of equation estimated by using linear interpolation between two points of function at each end of interval. In most cases, the convergence speed of this method is better than the bisection method. Figure 1 shows the linear interpolation method in brief.



Fig. 1.  The linear interpolation method


The algorithm of the linear interpolation method is as follows:


Step 1: Choose a and b so that f(a).f(b)<0.

Step 2: Let c=a - f(a).(b-a)/(f(b) - f(a)).

Step 3: If  f(a).f(c)<0  then let  b=c, else let  a=c.

Step 4: if |a-b|<e  then let root = a - f(a).(b-a)/(f(b) - f(a)), else go to step 2.

Step 5: End.


e: Acceptable approximated error.

Roots of Equation                                         
   (Source Code in C++)                                                         
o        Bisection Method                                                                                                   

o        Linear Interpolation Method                                                                           

o        Modified Methods                                                                                                 

o        Newton-Raphson Method                                                                                 

o        One point Interpolation Method                                                                   

o        Secant Method