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.

#### Newton-Raphson Formula

#### Newton-Raphson Algorithm

1 2 3 4 5 6 | 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | #include<stdio.h> #include<stdlib.h> float allowed_error = 0; double function(double value); double derived_function(double value); void newton_raphson_method(double value); int main() { double value; printf("\nEnter a Value:\t"); scanf("%lf", &value); printf("\nEnter Allowed Error:\t"); scanf("%f", &allowed_error); newton_raphson_method(value); return 0; } 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); } |

#### Output

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**.