Hello, i have done the following code in c++ which gives me a result but :(adsbygoogle = window.adsbygoogle || []).push({});

1) I compute the product "prod*=(y-x)/(x[k]-x)" which has variable "y" inside ,but the result i take is just a number.(i want the result to be for example in this form "p(x)=1.02*x^3+2*x^2..."

I can't understand how the program manipulates the variable y which does hasn't a value!

2) I don't know if i have it right..

The exercise is :

Find Lagrange's polynomial approximation for y(x)=cos(π x), x ∈−1,1 using 5 points

(x = -1, -0.5, 0, 0.5, and 1).

My code :

Code (Text):

using namespace std;

const double pi=3.1415;

// my function

double f(double x){

return (cos(pi*x));

}

//function to compute lagrange polynomial

double lagrange_polynomial(int N){

//N = degree of polynomial

double *x;//hold the values

x=new double [N+1];

int i,k;

double y;

//these points are given

x[0]=-1.0;

x[1]=-0.5;

x[2]=0;

x[3]=0.5;

x[4]=1.0;

//computations for finding lagrange polynomial

double sum=0;

for (k=0;k<=N;k++){

double prod=1.0;

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

if (i==k) prod=1.0;

else if (i!=k){

prod*=(y-x[i])/(x[k]-x[i]);

}

}

sum+=prod*f(x[k]);

}

return sum;

}

int main()

{

double deg,result;

cout <<"Give the degree of the polynomial :"<<endl;

cin >>deg;

result=lagrange_polynomial(deg);

cout <<"The Lagrange approximation is :"<<endl;

cout <<"p(x) = "<<result;

return 0;

}

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# Lagrange approximation

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