Newton Raphson Method Algorithm

Newton Raphson Method is open method and starts with one initial guess for finding real root of non-linear equations.

In Newton Raphson method if x0 is initial guess then next approximated root x1 is obtained by following formula:

x1 = x0 - f(x0) / g(x0)

And then process is repeated i.e. we use x1 to find x2 and so on until we find the root within desired accuracy.

Algorithm for Newton Raphson Method

1. Start

2. Define function as f(x)

3. Define first derivative of f(x) as g(x)

4. Input initial guess (x0), tolerable error (e) 
   and maximum iteration (N)

5. Initialize iteration counter i = 1

6. If g(x0) = 0 then print "Mathematical Error" 
   and goto (12) otherwise goto (7) 

7. Calcualte x1 = x0 - f(x0) / g(x0)

8. Increment iteration counter i = i + 1

9. If i >= N then print "Not Convergent" 
   and goto (12) otherwise goto (10) 

10. If |f(x1)| > e then set x0 = x1 
    and goto (6) otherwise goto (11)

11. Print root as x1

12. Stop

Recommended Readings

  1. Newton Raphson Method Algorithm
  2. Newton Raphson Method Pseudocode
  3. Newton Raphson Method Using C
  4. Newton Raphson Method Using C++
  5. Newton Raphson Method Online Calculator