Question

Using Newton-Raphson method, find the complex root of the function f(z) = z 2 + z + 1 with with an accuracy of 10–6. Let z0 = 1 − i. write program c++ or matlab

Answer 1

/* Program Newton-Raphson
Program to find a root of the equation x*x+x+1=0 by Newton-
Raphson method. f(x) and its derivative fd(x) are to be supplied. */
#include<stdio.h>
#include<math.h>
#include<stdlib.h>
void main()
{
int k=0; /* counts number of iterations */
float x1,x0; /* x0 is the initial guess */
float eps=1e-5; /* error tolerance */
float f(float x);
float fd(float x);
printf("\nEnter the initial guess x0 ");
scanf("%f",&x0);
x1=x0;
do
{
k++;
x0=x1;
x1=x0-f(x0)/fd(x0);
}while(fabs(x1-x0)>eps);
printf("One root is %8.5f obtained at %d th iteration ",x1,k);
} /* main */
/* definition of the function f(x) */
float f(float x)
{
return(x*x+x+1);
}
/* definition of the function fd(x) */
float fd(float x)
{
return(2*x*+1);
}