Newton Raphson Formula

Newton Raphson Interpolation Formula implementation in C.

Code:

#include <stdio.h>
#include <conio.h>
#define N 100
float comb(float,int);

/*****************************************************************/
/*****  Newton-raphson-interpolation formula implementation  *****/
/*****   This program uses the forward difference formula    *****/
/*****************************************************************/

void main()
{
	/* y=y[0]+rC1*dely[0]+rC2*del2y[0]+rC3*del3y[0]+...+rCn*delny[0] */
	/* where r is given as ==>  x=x[0]+r*h */
	float x[N],y[N],n,temp[N],res,r,X,h;
	int i,j;
	char ch;
	do
	{
		printf("\nEnter the total number of points for interpolation\n");
		scanf("%f",&n);
		printf("\nEnter the values of x\n");
		for(i=0;i<n;i++)
			scanf("%f",&x[i]);
		h=x[1]-x[0];
		printf("\nEnter the values of y\n");
		for(i=0;i<n;i++)
			scanf("%f",&y[i]);
		res=y[0];
		printf("\nEnter the values of x to find y\n");
		scanf("%f",&X);
		r=(X-x[0])/h;
		for(i=1;i<n;i++)
		{
			for(j=0;j<n;j++)
				temp[j]=y[j+1]-y[j];
			for(j=0;j<n;j++)
				y[j]=temp[j];
			res=res+comb(r,i)*temp[0];
		}
		printf("\nThe answer is %g\n",res);
		printf("\nDo you wish to continue[y/n]\n");
		ch=getche();
	}while(ch=='Y' || ch=='y');
	printf("\nPress any key to exit\n");
}

float comb(float n,int r)
{
	int i;
	float res=1;
	for(i=1;i<=r;i++)
		res=res*(n-i+1)/i;
	return(res); 
}

The code below finds the root of linear algebraic any order equation by "Newton-Raphson" method

Code:

#include <stdio.h>
#include <conio.h>
#include <math.h>
#include <stdlib.h>

#define ACC 0.01
#define N 10

int degree;

float coeff[N];
void input(void);
float F(float);
float dF_dx(float);

/********************************************************/
/*****  Finds the root of any linear algebraic any  *****/
/*****  order equation by "Newton-Raphson"  method  *****/
/********************************************************/

void main()
{
	char ch;
	do
	{
		input();
		printf("Do you wish to continue[y/n]\n");
		fflush(stdin);
		scanf("%c",&ch);
	}while(ch=='Y' || ch=='y');
}

void input(void)
{
	int i,print,loop=0;
	float ig;
	float h;
	printf("\nEnter the degree of diferential equation\n");
	scanf("%d",&degree);
	print=degree;
	for(i=0;i<=degree;i++)
	{
		printf("Enter the co-efficient of x to the power of %d\t",print--);
		scanf("%f",&coeff[i]);
	}
	printf("\nEnter the initial guess\n");
	scanf("%f",&ig);
	if(F(ig)==0)
		printf("\n%f  is the root of the equation\n",ig);
	do
	{
		h=-(F(ig))/(dF_dx(ig));
		ig=ig-h;
		loop++;
		if(loop>=40)
			exit(0);
	}while(fabs(h)>=ACC);
	printf("\n%f  is the root\n",ig);
}

float dF_dx(float x)
{
	int i,deg;
	float func=0.0;
	deg=degree;
	for(i=0;i<degree;i++)
	{
		func=func+coeff[i]*deg*pow(x,(deg-1));
		deg--;
	}
	if(func==0)
		return(1);
	return(func);
}

float F(float x)
{
	int i,deg;
	float func=0.0;
	deg=degree;
	for(i=0;i<=degree;i++)
	{
		func=func+coeff[i]*pow(x,deg);
		deg--;
	}
	return(func);
}

 

Same here : code does not conform to ANSI C specifications !

 

I know the formula but can't derive it from the Newton-Raphson's method of finding roots of f(x)=0.

the formula that I know is x1 = x0 - k * f(x0) / f`(x0)
where k = number of times a single root is repeating for f(x) = 0.

plz help!!

 

Great work !
Well done ! !Keep it up ! !