Trying to implement Durand-Kerner-Method in C++ using Matrices

Question

My implementation of the Durand-Kerner-Method (https://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method) does not seem to work. I believe (see following code) that I am not calculating new approximation correctly in the algorithm part itself. I cannot seem to be able to fix the problem. Very grateful for any advice.

#include <complex>
#include <cmath>
#include <vector>
#include <iostream>
#include "DurandKernerWeierstrass.h"

using namespace std;
using Complex = complex<double>;
using vec = vector<Complex>;
using Matrix = vector<vector<Complex>>;


//PRE: Recieves input value of polynomial, degree and coefficients
//POST: Outputs y(x) value
Complex Polynomial(vec Z, int n, Complex x) {

    Complex y = pow(x, n);
    for (int i = 0; i < n; i++){
        y += Z[i] * pow(x, (n - i - 1));
    }
    return y;
}

/*PRE: Takes a test value, degree of polynomial, vector of coefficients and the desired
precision of polynomial roots to calculate the roots*/
//POST: Outputs the roots of Polynomial

Matrix roots(vec Z, int n, int iterations, const double precision) {
    Complex z = Complex(0.4, 0.9);
    Matrix P(iterations, vec(n, 0));
    Complex w;
    
    //Creating Matrix with initial starting values
    
    for (int i = 0; i < n; i++) {
        P[0][i] = pow(z, i);
    }

    //Durand Kerner Algorithm

    for (int col = 0; col < iterations; col++) {

        *//I believe this is the point where everything is going wrong*

        for (int row = 0; row < n; row++) {
            Complex g = Polynomial(Z, n, P[col][row]);
            for (int k = 0; k < n; k++) {
                if (k != row) {
                    g = g / (P[col][row] - P[col][k]);
                }

            }
                
            P[col][row] -= g;

        }
            
        return P;
    }   
    

}

The following Code is the code I am using to test the function:

int main() {
    //Initializing section

    vec A = {1, -3, 3,-5 };
    int n = 3;
    int iterations = 10;
    const double precision = 1.0e-10;
    Matrix p = roots(A, n, iterations,precision);
    for (int i = 0; i < iterations; i++) {
        for (int j = 0; j < n; j++) {
            cout << "p[" << i << "][" << j << "] = " << p[i][j] << " ";
            
        }
        cout << endl;
    }
    return 0;

}

Important to note the Durand-Kerner-Algorithm is connected to a header file which is not included in this code.

Answer 1

Your problem is that you do not transcribe the new values into the next data record with index col+1. Thus in the next loop you start again with a data set of zero entries. Change to

        P[col+1][row] = P[col][row] - g;

If you want to use the new improved approximation immediately for all following approximations, then use

        P[col+1][row] = (P[col][row] -= g);

Then the data sets all contain the next approximations, especially the first one will no longer contain the initially set powers.