**C program of Newton Raphson Method** : **Newton Raphson method** is a method of approximating a root of the polynomial equation also called the method of tangents. In Newton’s method, the initial (“first”) approximation *x* = *a*_{1} is used to find a second, more accurate, approximation by drawing the tangent to the graph of *y* = *f(x*) at the point *A[a*_{1}, *f(a*_{1})] up to the intersection of the tangent with the *x*-axis. The point of intersection is

* x* = *a*_{1} – *f(a*_{1})/*f*’(*a*_{1})

and is adopted as the new value *a*_{2} of the root. By repeating this process as necessary, we can obtain increasingly accurate approximations *a*_{2}, *a*_{3}, … of the root provided that the derivative *f*’(*x*) is monotonic and preserves its sign on the segment containing *root*.

How to use the **C program** :

Consider an example : f(x) = x^2 – 4 as our polynomial equation. We want to calculate its root and say first approximation =6. Then maximum power of X = 2, coefficients of x^0 = -4, x^1 = 0, x^2 = 1 & first approximation =6. Now **C program of Newton Raphson Method** will display the iterations and root of the polynomial as output.

### C program of Newton Raphson Method :

#include<conio.h> #include<stdio.h> #include<stdlib.h> #include<math.h> int max_power,i=0,cnt=0,flag=0; int coef[10]={0}; float x1=0,x2=0,t=0; float fx1=0,fdx1=0; int main() { printf("-----------------------------------------------------------\n"); printf("----------------------Made by C code champ-----------------\n"); printf("-----------------------------------------------------------\n\n"); printf("\n\n\t C PROGRAM FOR NEWTON RAPHSON METHOD"); printf("\n\n\n\tENTER THE MAXIMUM POWER OF X = "); scanf("%d",&max_power); for(i=0;i<=max_power;i++) { printf("\n\t x^%d = ",i); scanf("%d",&coef[i]); } printf("\n"); printf("\n\tTHE POLYNOMIAL IS = "); for(i=max_power;i>=0;i--)/*printing coefficients*/ { printf(" %dx^%d",coef[i],i); } printf("\n\n\tFirst approximation x1 ----> "); scanf("%f",&x1); printf("\n\n-----------------------------------------------------------\n"); printf("\n ITERATION \t x1 \t F(x1) \t \tF'(x1) "); printf("\n-----------------------------------------------------------\n"); do { cnt++; fx1=fdx1=0; for(i=max_power;i>=1;i--) { fx1+=coef[i] * (pow(x1,i)) ; } fx1+=coef[0]; for(i=max_power;i>=0;i--) { fdx1+=coef[i]* (i*pow(x1,(i-1))); } t=x2; x2=(x1-(fx1/fdx1)); x1=x2; printf("\n\t %d \t%.3f \t %.3f\t\t%.3f ",cnt,x2,fx1,fdx1); }while((fabs(t - x1))>=0.0001); printf("\n\n\n\t THE ROOT OF EQUATION IS = %f",x2); getch(); }

We hope that you all have enjoyed the C program of Newton Raphson Method. If you have any doubts related to the program ask us in form of comments.

testing…

comments level two testing..

It is very useful for the Beginners.

thanks!

very useful:)…thanks:)

Great blog but maybe you should get up and stand up

Where is the output screen with the root?

lmao! My feelings exactly! What is the world coming to?

You made some respectable points there. I scoured on the web for the issue and located most individuals will associate with with your website.

it would be more useful if explanation for every line is given after the program

i mean functions of different statements