Gauss-Seidel method

#include <iostream>
#include <vector>
#include <math.h>

using namespace std;

bool converges(vector < vector <double> > A){
    int N = A.size();

    for(int i = 0; i < N; ++i){
        double sum = 0;

        for(int j = 0; j < N; ++j){
            if(j != i){
                sum += fabs(A[i][j]);
            }
        }

        if(fabs(A[i][i]) <= sum){
            return false;
        }
    }

    return true;
}

bool stop(vector <double> x, vector <double> x_prev, double Eps){
    int N = x.size();

    for(int i = 0; i < N; ++i){
        if(fabs(x[i] - x_prev[i]) >= Eps){
            return false;
        }
    }

    return true;
}

vector <double> Gauss_Seidel(vector < vector <double> > A, vector <double> b, double Eps){
    int N = A.size();
    vector <double> x(N), x_prev(N);

    do{
        x_prev = x;

        for(int i = 0; i < N; ++i){
            double sum = 0;

            for(int j = 0; j < i; ++j){
                sum += A[i][j] * x[j];
            }
            for(int j = i + 1; j < N; ++j){
                sum += A[i][j] * x_prev[j];
            }
            x[i] = (b[i] - sum) / A[i][i];
        }
    }
    while(!stop(x, x_prev, Eps));

    return x;
}

int main(){
    int N;
    cin >> N;

    vector < vector <double> > A(N, vector <double> (N));
    vector <double> b(N);

    for(int i = 0; i < N; ++i){
        for(int j = 0; j < N; ++j){
            cin >> A[i][j];
        }
        cin >> b[i];
    }

    if(!converges(A)){
        cout << "The matrix does not have diagonal predominance!";
        system("PAUSE");
        return 0;
    }

    double Eps = 1e-5;
    cin >> Eps;

    for(auto & x : Gauss_Seidel(A, b, Eps)){
        cout << x << endl;
    }

    system("PAUSE");
    return 0;
}