Методы вычислений 09.09.22

#include <iostream>
#include <iomanip>
#include <vector>
#include <cmath>
using namespace std;

vector <int> x, y;

double P(double x)
{
    return (-x * x * x / 6.0) + (3 * x * x / 2.0) - (x / 3.0) + 10.0;
}

double L(double x0)
{
    double res = 0;

    for (int i = 0; i < x.size(); ++i)
    {
        double cur = 1.0;

        for (int j = 0; j < y.size(); ++j)
            if (i != j) cur *= (x0 - x[j]) / (x[i] - x[j]);

        res += y[i] * cur;
    }

    return res;
}

double N(double x0)
{
    vector <vector <double>> table(y.size(), vector <double>(y.size()));

    for (int i = 0; i < y.size(); ++i)
        table[i][0] = y[i];

    for (int j = 1; j < y.size(); ++j)
        for (int i = 0; i < y.size() - j; ++i)
            table[i][j] = (table[i + 1][j - 1] - table[i][j - 1]) / (x[i + j] - x[i]);

    double res = 0.0, cur = 1.0;

    for (int j = 0; j < y.size(); ++j)
    {
        res += table[0][j] * cur;
        cur *= (x0 - x[j]);
    }

    return res;
}

int main()
{
    cout << fixed << setprecision(4);

    x = { 0, 1, 2, 3 };
    y = { 10, 11, 14, 18 };

    cout << left << setw(10) << "x";

    for (int i = 0; i < x.size() - 1; ++i)
        cout << setw(10) << x[i] + 0.5;

    cout << "\n" << left << setw(10) << "P(x)";

    for (int i = 0; i < x.size() - 1; ++i)
        cout << setw(10) << P(x[i] + 0.5);

    cout << "\n" << left << setw(10) << "L(x)";

    for (int i = 0; i < y.size() - 1; ++i)
        cout << setw(10) << L(x[i] + 0.5);

    cout << "\n" << left << setw(10) << "N(x)";

    for (int i = 0; i < y.size() - 1; ++i)
        cout << setw(10) << N(x[i] + 0.5);

    return 0;
}