Let us learn how to implement Newton Raphson method in C programming with its explanation, advantages, output and much more.
What is Newton-Raphson’s Method?
The newton raphson algorithm is one of the most popular root-finding methods. So, it is basically used to find roots of a real-valued function.
This method is named after Isaac Newton and Joseph Raphson and is used to find a minimum or maximum of a function.
The Newton’s method is a better approximation method as compared to some other numerical methods. It is based on the idea of simple linear approximation.
This is a one-point method since it requires only one starting value and does not need to satisfy any other serious conditions.
Step 1: Calculate values of derived_function(value) and function(value)
Step 2: Calculate m = function(value) / derived_function(value)
Step 3: While m is greater than the allowed error
m = function(value) / derivfunction(value)
Step 4: value = value - m
Step 5: Evaluated Result
Flowchart For Newton – Raphson Method
Advantages of Newton Raphson Method
- The number of significant digits doubles after every iteration which brings us more closer to the root.
- The Newton – Raphson method converges faster than Bisection method and False Position Method.
- This method converges quadratically on the root which enables this algorithm to deal with the higher degree of variable involved.
Note: This C program for Newton – Raphson method in numerical analysis is compiled with GNU GCC compiler using CodeLite IDE on Microsoft Windows 10 operating system.
C Program For Newton Raphson Method
float allowed_error = 0;
double function(double value);
double derived_function(double value);
void newton_raphson_method(double value);
printf("\nEnter a Value:\t");
printf("\nEnter Allowed Error:\t");
void newton_raphson_method(double value)
double m = function(value) / derived_function(value);
for ( ;abs(m) >= allowed_error; )
m = function(value) / derived_function(value);
value = value - m;
printf("\nRoot Value:\t%f\n", value);
double function(double value)
return (value * value * value - value * value + 2);
double derived_function(double value)
return (3 * value * value - 2 * value);
If you have any doubts about the implementation of Newton Raphson rule formula in C programming, let us know about it in the comment section. Find more about it on Wikipedia.