C Program for Newton Raphson Method. In the c programming language, this program implements the Newton Raphson method for finding the real root of a nonlinear equation. The Newton–Raphson technique, named after Isaac Newton and Joseph Raphson, is a root-finding procedure in numerical analysis that gives successively improved approximations to the roots of a real-valued function.

#include<stdio.h>

#include<conio.h>

#include<math.h>

#include<stdlib.h>

#define f(x) 3*x - cos(x) -1

#define g(x) 3 + sin(x)

void main()

{

float x0, x1, f0, f1, g0, e;

int step = 1, N;

clrscr();

printf("\nEnter initial guess\n");

scanf("%f", &x0);

printf("Enter tolerable error\n");

scanf("%f", &e);

printf("Enter maximum iteration\n");

scanf("%d", &N);

printf("\nStep\t\tx0\t\tf(x0)\t\tx1\t\tf(x1)\n");

do

{

g0 = g(x0);

f0 = f(x0);

if(g0 == 0.0)

{

printf("Mathematical Error");

exit(0);

}

x1 = x0 - f0/g0;

printf("%d\t\t%f\t%f\t%f\t%f\n",step,x0,f0,x1,f1);

x0 = x1;

step = step+1;

if(step > N)

{

printf("Not Convergent");

exit(0);

}

f1 = f(x1);

}

while(fabs(f1)>e);

printf("\nRoot is %f", x1);

getch();

}

## C Program for Newton Raphson Method is Fast and Why

The Newton technique is a higher-order method that results in a more accurate approximation of your function. In most cases, the Newton technique precisely minimises the second order approximation of a function f.

The Newton–Raphson technique is a root-finding algorithm named after Isaac Newton and Joseph Raphson that gives successively improved approximations to the roots of a real-valued function.

## Math Header File in C

math. h is a header file in the C programming language’s standard library that is used for basic mathematical operations. The majority of the functions make use of floating point numbers. A math function is defined as a relationship that maps elements from one set (A) to another (B), with each element of the first set mapped to only one element of the second set.

## Stdlib.h in C to Execute Program for Newton Raphson Method

stdlib. h is a general-purpose standard header that includes Dynamic Memory Allocation functions and other Standard Functions. The getch() function necessitates the inclusion of the stdlib header.

## Data Types in C Program

In C, data types refer to a comprehensive system for declaring variables or functions of various types. A variable’s type determines how much storage space it takes up and how the bit pattern stored is interpreted.

A data type is a property associated with a piece of data that instructs a computer system on how to interpret its value. Understanding data types ensures that data is collected in the desired format and that each property’s value is as expected.