牛顿插值求解多项式

#include <iostream>

using namespace std;

//牛顿插值求解多项式

double * xs;   //all input x

double * ys;   //all input y

int n;      //size

//1 2 3 4

//0 -5 -6 3

//1.5

//-2.625

void init()

{

cout << "please input n " << endl;

cin >> n;

xs = new double[n];

ys = new double[n];

//input x

cout << "please input the x's value !" << endl;

for(int i=0; i<n; i++)

{

cin >> xs[i];

}

//input y

cout << "please input the y's value !" << endl;

for(int i=0; i<n; i++)

{

cin >> ys[i];

}

}

double f(int n)

{

double f=0;

double temp=0;

for(int i=0; i<n+1; i++)

{

temp=ys[i];

for(int j=0; j<n+1; j++)

{

if(i!=j)

temp /= (xs[i]-xs[j]);

}

f += temp;

}

return f;

}

double newton(double x)

{

double result=0;

for(int i=0; i<n; i++)

{

double temp=1;

double fi=f(i);

for(int j=0; j<i; j++)

{

temp = temp*(x-xs[j]);

}

result += fi*temp;

}

return result;

}

int main()

{

init();

double x;

cout << "please input the x' value !" << endl;

cin >> x;

cout << "the result of the Newton is " << newton(x);

return 0;

}

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