Question

Develop an alternative formulation for calculating the polynomial expression that avoids the need for repeated power calculation and reduces the risk of numerical instability

(iv) In calculating the value of a polynomial function f(x) anx" an-1x" 1 ao in C++ it is unwieldy to repeatedly calculate x Develop an alternative formulation for calculating the polynomial expression that avoids the need for repeated power calculation and reduces the risk of numerical instability. (You may describe your formulation using C/C++ syntax if you wish.)

Answer 1

#include <bits/stdc++.h>
#define max 10
using namespace std;

int main()
{
int ar[max];
int i, num, power;
float x, result;

cout<<"Enter the order of the polynomial \n";
cin>>num;
cout<<"Enter the value of x \n";
cin>> x;
cout<<"Enter " <<num + 1<< "coefficients \n";
for (i = 0; i <= num; i++)
{
cin>>ar[i];
}
result = ar[0];
for (i = 1; i <= num; i++)
{
result = result * x + ar[i];
}
power = num;

cout<<"Polynomial is: \n";
for (i = 0; i <= num; i++)
{
if (power < 0)
{
break;
}

if (ar[i] > 0)
cout<<" + ";
else if (ar[i] < 0)
cout<<" - ";
else
cout<<" ";
cout<<abs(ar[i])<<"x^" <<(power--);
}
cout<<"\n Value of the polynomial = "<<result;
}

===================================================================

akshay@akshay-Inspiron-3537:~/Chegg$ ./a.out
Enter the order of the polynomial
2
Enter the value of x
2
Enter 3 coefficients
3
2
6
Given polynomial is:
+ 3x^2 + 2x^1 + 6x^0
Value of the polynomial = 22