Текст программы. Предварительные вычисления

Предварительные вычисления

Найдем производную

График функции

Преобразуем функцию к следующему виду

Ее график

Таким образом, интервалы, на которых ищем нули функции: .

#include <cstdio>

#include <cstring>

#include <cstdlib>

#include <cmath>

#include <iostream>

#include <iomanip>

long double function_1_3_22(const long double &x)

{

//f(x) = cos(x, 0.3) - x^2

return (cos(x + 0.3) - x*x);

}

long double D_function_1_3_22(const long double &x)

{

//f(x) = cos(x, 0.3) - x^2

return (- sin(x + 0.3) - 2*x);

}

namespace method

{

long double Bisection_Method(long double (*func)(const long double&), long double a, long double b, long double epsilon, long double &x, long double &y, unsigned __int64 &i)

{

long double c = (a + b)/(long double)2;

for (i = 1; std::abs(b - a) >= epsilon; ++i)

{

if (func(a)*func(c) < 0) b = c;

else a = c;

c = (a + b)/(long double)2;

}

x = c;

y = func(x);

}

void Secant_Method(long double (*func)(const long double&), long double a, long double b, long double epsilon, long double &x, long double &y, unsigned __int64 &i)

{

long double c = a - func(a)*(b - a)/(func(b) - func(a));

for (i = 1; std::abs(func(a)) >= epsilon; ++i)

{

a = c;

c = a - func(a)*(b - a)/(func(b) - func(a));

}

x = c;

y = func(x);

}

void Tangent_Method(long double (*func)(const long double&), long double (*D_func)(const long double&), long double a, long double b, long double epsilon, long double &x, long double &y, unsigned __int64 &i)

{

long double c = b - func(b)/D_func(b);

for (i = 1; std::abs(func(b)) >= epsilon; ++i)

{

b = c;

c = b - func(b)/D_func(b);

}

x = c;

y = func(x);

}

void Secant_And_Tangent_Method(long double (*func)(const long double&), long double (*D_func)(const long double&), long double a, long double b, long double epsilon, long double &x, long double &y, unsigned __int64 &i)

{

long double a1 = a - func(a)*(b - a)/(func(b) - func(a));

long double b1 = b - func(b)/D_func(b);

for (i = 1; std::abs(b1 - a1) >= epsilon; ++i)

{

a = a1;

b = b1;

a1 = a - func(a)*(b - a)/(func(b) - func(a));

b1 = b - func(b)/D_func(b);

}

x = (std::abs(a1) < std::abs(b1))? a1: b1;

y = func(x);

}

}

int main(int argc, char** argv)

{

const long double epsilon = 0.0001;

long double x,y;

unsigned __int64 count_of_iteration;

std::cout << std::fixed << std::setw(20) << std::setprecision(15);

method::Bisection_Method(function_1_3_22, 0, M_PI_2, epsilon, x, y, count_of_iteration);

std::cout << "Bisection Method\t" << x << "\t" << y << "\t" << count_of_iteration << std::endl;

method::Secant_Method(function_1_3_22, 0, -M_PI, epsilon, x, y, count_of_iteration);

std::cout << "Secant Method\t\t" << x << "\t" << y << "\t" << count_of_iteration << std::endl;

method::Secant_Method(function_1_3_22, 0, M_PI, epsilon, x, y, count_of_iteration);

std::cout << "Secant Method\t\t" << x << "\t" << function_1_3_22(x) << "\t" << count_of_iteration << std::endl;

method::Tangent_Method(function_1_3_22, D_function_1_3_22, 0, -M_PI, epsilon, x, y, count_of_iteration);

std::cout << "Tangent Method\t\t" << x << "\t" << y << "\t" << count_of_iteration << std::endl;

method::Tangent_Method(function_1_3_22, D_function_1_3_22, 0, M_PI, epsilon, x, y, count_of_iteration);

std::cout << "Tangent Method\t\t" << x << "\t" << function_1_3_22(x) << "\t" << count_of_iteration << std::endl;

method::Secant_And_Tangent_Method(function_1_3_22, D_function_1_3_22, 0, -M_PI, epsilon, x, y, count_of_iteration);

std::cout << "Combined Method\t\t" << x << "\t" << y << "\t" << count_of_iteration << std::endl;

method::Secant_And_Tangent_Method(function_1_3_22, D_function_1_3_22, 0, M_PI, epsilon, x, y, count_of_iteration);

std::cout << "Combined Method\t\t" << x << "\t" << function_1_3_22(x) << "\t" << count_of_iteration << std::endl;

std::system("pause");

return 0;

}

Дата добавления: 2015-05-10