Newton's Method is
mainly used for finding the roots of a polynomial. This method is also known as
Newton Raphson method in the numerical analysis. We start with our approximated
root of a function in this method which further computes the better
approximation which is somewhere near the actual root.
Newton Raphson Method is
also known as Method of tangents. Let us now demonstrate how to use this
program:
Consider an example :
f(x)=9x^3-9 . we need to find root of this polynomial and we assume its root to
be 5. Now, max power of x will be 3 , x^0 = -9 , x^1 = 0 , x^2 = 0, x^3 = 9 and
first approximation = 5 . After entering such details according to our
polynomial , Newton Raphson C Program will display the root of polynomial and
iterations as the output.
#include
#include
#include
#include
int maxpow,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 NEWTON RAPHSON
METHOD");
printf("\nENTER THE MAXIMUM POWER
OF X = ");
scanf("%d",&maxpow);
for(i=0;i<=maxpow;i++)
{
printf("\n
x^%d = ",i);
scanf("%d",&coef[i]);
}
printf("\n");
printf("\nYour polynomial is
= ");
for(i=maxpow;i>=0;i--)
{
printf("
%dx^%d",coef[i],i);
}
printf("\nFirst 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=maxpow;i>=1;i--)
{
fx1+=coef[i]
* (pow(x1,i)) ;
}
fx1+=coef[0];
for(i=maxpow;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 THE ROOT OF EQUATION IS
= %f",x2);
getch();
}
