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Wednesday, 2 April 2014

LAGRANGE’S INTERPOLATION using c++.

Example-

Find the vaiue of f(153)for the given table.
 y=f(x)

                         x                                 y=f(x)

                       150                              12.247
                       152                               12.329
                       154                                     12.410
                          156                                     12.490


C++ implementation of Lagrange's interpolation-

#include iostream .h
#include stdio.h
#include conio.h
#include math.h
void main()
{
    float x[10],y[10],temp=1,f[10],sum,p;
     int i,n,j,k=0,c;
     clrscr();
     cout<<" how many record you will enter:";
     cin>>n;
     for(i=0;i>x[i];
     cout<<"enter the value of y["<>y[i];
  }
     cout<<"enter the x for finding f(x):";
     cin>>p;
     for(i=0;in;i++)
   {
     cout<<"enter the value of x["<<i<<"]";
     cin>>x[i];
     cout<<"enter the value of y["<<i<<"]";
     cin>>y[i];
  }
     cout<<"enter the x for finding f(x):";
     cin>>p;
     for(i=0;i<n;i++)
	{
	temp=1;
	 k=i;
		for(j=0;j<n;j++)
		 {
		      if(k==j)
		  	continue;
		     else
			    temp=temp*((p-x[j])/(x[k]-x[j]));
		    f[i]=y[i]*temp;
		  }
  for(i=0;i<n;i++)
     sum=sum+f[i];
   cout<<"the value of f["<<p<<"]="<<sum;
   getch();
   }

OUTPUT-

how many record you will enter:4

enter the value of x[0]=150
enter the value of y[0]=12.247
enter the value of x[1]=152
enter the value of y[1]=12.329
enter the value of x[2]=154
enter the value of y[2]=12.410
enter the value of x[3]=156
enter the value of y[3]=12.490
enter the x for finding f(x)=153
the value of f[153]=12.369625

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