appr newton

#include "pch.h"
#include <iostream>
#include <iomanip>
#include <math.h>
using namespace std;

double func(double x) {
    return pow(x, 2) - 10 * pow(sin(x), 2);
}

double Newton(double x, double**& XYtable, int n)
{
    double result = XYtable[0][1];
    double ind = 1;
    double* diff = new double[20];
    for (int i = 0; i < n; i++) {
        diff[i] = XYtable[i][1];
    }
    for (int i = 0; i < n - 1; i++) {
        for (int j = 0; j < (n - 1) - i; j++) {
            diff[j] = (diff[j + 1] - diff[j]) / (XYtable[j + i + 1][0] - XYtable[j][0]);
        }
        ind *= x - XYtable[i][0];
        result += ind * diff[0];
    }
    return result;
}
int main(void)
{
    setlocale(LC_ALL, "Russian");
    cout << "Введите границы a и b " << endl;
    int a, b;
    cin >> a >> b;
    cout << "Введите m " << endl;
    int m;
    cin >> m;
    double** matr = new double*[20];
    for (int i = 0; i < 20; i++)matr[i] = new double[2];
    int k = 0;
    for (double i = a; i <= b; i += (b - a) / (m - 1)) {
        matr[k][0] = i;
        matr[k][1] = func(i);
        k++;
    }
    cout << setw(4) << "X" << setw(10) << "Y" << endl;
    for (int i = 0; i < k; i++) {
        cout<< setw(4) << matr[i][0] << setw(10) << matr[i][1] << endl;
    }
    cout << endl;
    cout << setw(5) << "X" << setw(10) << "Y" <<setw(10)<<"P"<<setw(12)<<"погр."<< endl;
    for (int i = 0; i < 21; i++) {
        double temp = a + ((b - a) / 20.)*i;
        cout << setw(5) << temp << setw(10) << func(temp) << setw(10) << Newton(temp, matr,m) << setw(12) << fabs(func(temp)- Newton(temp, matr, m)) << endl;
    }
    return 0;
}