Horner's Method

Horner's Method

There are two common methods of expressing polynomial functions, power basis and Bézier. Although mathematically equivalent, we will see that the Bézier method is far better suited to representing and manipulating shape in a computer.

Horner’s method is most efficiently computed by giving  and the point  on a power basis curve.

 

 

include <iostream>

using namespace std;

int main(){

 

// ..........................................................................//

             //sum: the sum of the equation if we give the value of the u.

             //a: coefficient of power basis representation.

             //u: variable

             //degree: the formula will change based on the degree of function

             //function is f(u) = ao + a1(u) + a2(u^2)+ ... + an(u^n) for degree n

//..........................................................................//

       double sum[50]; //we want to store the degree only max=50

       double u, a[50];

       int degree;

       cout << "Degree = ";

       cin >> degree;

       if ( degree <= 0) {

             cout << "Degree must be bigger than 0 \n\n" << "Please input the degree again, degree = ";

             cin >> degree;

      }

       else {

             cout << "Please input the u value -> u =";

             cin >> u;

             cout << "Please input coefficients (a)" << degree << "= ";

             cin >> a[degree];

             cout << "Please input coefficients (a)" << degree – 1 << "= ";

             cin >> a[degree - 1];

       }

       sum[degree] = a[degree] * u + a[degree - 1];

       for (int i = degree; i > 1; i--){

            cout << "Please input coefficients (a)" << i - 2 << "= ";

            cin >> a[i - 2];

            sum[i - 1] = (sum[i] * u + a[i - 2]);

       }

       cout << "Function is: f(u) = ";

       for (int i = degree; i > 0; i--){

             cout << a[i] << "*u^" << i << "+";

       }

       cout << a[0] << endl;

       cout << "Horner result is: f(" << u << ")=" << sum[1] << endl;

       system("pause");

       return 0;

}