lab2.cpp

using namespace std;

#include <cstdio>
#include <cmath>
#include <vector>

double function(double x) {
    return log(x) - x + 5;
}

double derivative(double x) {
    return 1.0 / x - 1;
}

vector<int> iteration(double X, double step) {
    double a = X, b = X + step;
    double da = derivative(a), db = derivative(b), m, M;

    if (abs(da) >= abs(db)) {
        M = da;
        m = db;
    } else {
        M = db;
        m = da;
    }

    double q = 1 - abs(m / M);

    vector<int> iterations;
    printf("|  eps  |     equation root     | accuracy estimation I |\n");
    for (double eps = 1E-2; eps > 1E-14; eps *= 1E-3) {
        double t = (1 - q) / q * eps;
        double x = (a + b) / 2, x1 = x;
        int count = 0;
        do {
            x = x1;
            x1 = x - function(x) / M;
            count++;
        } while (abs(x1 - x) > t);
        iterations.push_back(count);
        printf("| %.0E | %13.19f | %.19f |\n", eps, x1, abs(abs(x1) - abs(x)) * q / (1 - q));
    }
    printf("\n");
    return iterations;
}

vector<int> secant(double A, double B, double step) {
    vector<int> iterations;
    printf("|  eps  |     equation root     | accuracy estimation S |\n");
    for (double eps = 1E-2; eps > 1E-14; eps *= 1E-3) {
        double a = A, b = B, x;
        int count = 0;
        while (fabs(b - a) >= eps) {
            x = a + (function(b) * (b - a)) / (function(b) - function(a));
            if (function(a) * function(x) < 0) {
                b = x;
            } else if (function(x) * function(b) < 0) {
                a = x;
            }
            count++;
        }

        iterations.push_back(count);
        printf("| %.0E | %13.19f | %.19f |\n", eps, x, abs((b - a) * 0.5));
    }
    printf("\n");
    return iterations;
}

vector<double> find_x(double a, double b, double step) {
    vector<double> X;
    for (double x = a; x <= b; x += step) {
        if (function(x) * function(x + step) < 0) {
            X.push_back(x);
        }
    }
    return X;
}

int main() {
    double step = 0.1;
    double a = 6.5;
    double b = 7.6;

    auto X = find_x(a, b, step)[0];

    vector<int> ii = iteration(X, step);
    vector<int> ib = secant(a, b, step);

    printf("|  eps  | iteration count | secant count |\n");
    int index = 0;
    for (double eps = 1E-2; eps > 1E-14; eps *= 1E-3, index++) {
        printf("| %.0E | %15i | %12i |\n", eps, ii[index], ib[index]);
    }
}