lab2

#include <iostream>
#include <cmath>

double AntiDerivative(double x) {
    return x * x + 2 * sin(x) - 1;
}

double FirstDerivative(double x) {
    return 2 * (x + cos(x));
}

double SecondDerivative(double x) {
    return 2 - 2 * sin(x);
}

double Phi(double x, double lambda) {
    return FirstDerivative(x) > 0.0 ? x - lambda * AntiDerivative(x) : x + lambda * AntiDerivative(x);
}

double Iterative(double a, double b, double eps, double &delta, unsigned int &iterations) {
    double m1, M1;
    if (fabs(FirstDerivative(a)) >= fabs(FirstDerivative(b))) {
        m1 = fabs(FirstDerivative(b));
        M1 = fabs(FirstDerivative(a));
    } else {
        m1 = fabs(FirstDerivative(a));
        M1 = fabs(FirstDerivative(b));
    }

    double xk = (a + b) * 0.5;
    double lambda = 1.0 / M1;
    double q = 1.0 - m1 * lambda;
    double t = q / (1 - q);
    iterations = 0;

    do {
        double x0 = xk;
        xk = Phi(x0, lambda);
        iterations++;
        delta = fabs(xk - x0) * t;
    } while (delta > eps);

    return xk;
}

double Tangets(double a, double b, double eps, double &delta, unsigned int &iterations) {
    double m1;
    if (fabs(FirstDerivative(a)) >= fabs(FirstDerivative(b))) {
        m1 = fabs(FirstDerivative(b));
    } else {
        m1 = fabs(FirstDerivative(a));
    }
    double xk = AntiDerivative(a) * SecondDerivative(a) > 0 ? a : b;
    iterations = 0;

    do {
        xk -= AntiDerivative(xk) / FirstDerivative(xk);
        iterations++;
        delta = fabs(AntiDerivative(xk)) / m1;
    } while (delta > eps);

    return xk;
}

void FindRoots(double a, double b, double step, double *X, int count) {
    int n = (int((b - a) / step) >> 1) << 1;
    step = (b - a) / (double) n;

    for (int i = 0, roots = 0; (i < n) && (roots < count); i++) {
        double x = a + i * step;
        if (AntiDerivative(x) * AntiDerivative(x + step) < 0) {
            X[roots++] = x;
        }
    }
}

int main() {
    double X[2];
    FindRoots(-2, 1, 0.1, X, 2);

    for (int i = 0; i < 2; i++) {
        double x = X[i];

        printf("|  eps  |      equation root      | Iterative accuracy |\n");
        for (double eps = 1e-2, delta = 0; eps > 1e-14; eps *= 1e-3) {
            unsigned int iterations;
            double y = Iterative(x, x + 0.1, eps, delta, iterations);
            printf("| %.0e | %23.20f | %.12e |\n", eps, y, delta);
        }
        printf("\n");
    }

    for (int i = 0; i < 2; i++) {
        double x = X[i];

        printf("|  eps  |      equation root      |  Tangets accuracy  |\n");
        for (double eps = 1e-2, delta; eps > 1e-14; eps *= 1e-3) {
            unsigned int iterations;
            double y = Tangets(x, x + 0.1, eps, delta, iterations);
            printf("| %.0e | %23.20f | %.12e |\n", eps, y, delta);
        }
        printf("\n");
    }

    printf("|  eps  | Iterative iteration | Tangets iteration |\n");
    for (double eps = 1e-2, delta, x = X[0]; eps > 1e-14; eps *= 1e-3) {
        unsigned int iterations1, iterations2;
        Iterative(x, x + 0.1, eps, delta, iterations1);
        Tangets(x, x + 0.1, eps, delta, iterations2);
        printf("| %.0e | %19d | %17d |\n", eps, iterations1, iterations2);
    }
    printf("\n");
}