Demonstration of Newtons Forward Interpolation Method

#include 'stdio.h'

float table[10][12];

int coordinates , i=0, j=0;

float sum =0.0 ;

int del;

int mark;

float p,x,y;

void calculate() {

while(1) {

printf("\n Enter a X-coordinate near the starting region .(Enter 99 to terminate) ....");

scanf("%f",&x);

if(x==99)

break;

p =  (x - table[0][0])/(table[1][0] - table[0][0]);

y = table[0][1] + p*table[0][2] + (p*(p-1)/2.0)*table[0][3] + (p*(p-1)*(p-2)/6.0)*table[0][4] + (p*(p-1)*(p-2)*(p-3)/24.0)*table[0][5] ;

printf("\n Calculated approximate value of Y(%f) is %f",x,y);

}

return ;

}

void printTable() {

/* PRINTING THE TABLE */

printf("\n\n\t THE FORWARD DIFFERENCE TABLE \n\n");

 for(i=0; i< coordinates ; i++) {

              for(j=0; j< mark-i ; j++) {

                         printf("    %f", table[i][j]);}

                                      printf("\n");}

calculate();

return;

}

void main() {

printf("\tEnter the number of coordinates ... \n\n");

scanf("%d",&coordinates);

for(i=0;i<10;i++) {

 for(j=0;j<10;j++) {

            table[i][j]=0.00;

            }}

for(i=0; i< coordinates ; i++) {

printf("\n\tEnter X(%d) and Y(%d) ... ",i,i);

scanf("%f %f",&table[i][0],&table[i][1]);

}

/* CALCULATING TABLE ELEMENTS */

for(del=2 ; del<=coordinates ; del++) {

 sum = 0.0;

              for(i=0; i<=(coordinates-(del-1)) ; i++) {

                        table[i][del] = table[i+1][del-1] - table[i][del-1] ;

                                    sum = sum + table[i][del] ;}

                                                  if(sum==0) {

                                                            mark = del;

                                                            printTable();

                                                            break;  }  }

if(sum !=0) {

mark = del;

printTable();}

}

Output: