Текст программы

#include <cstdio>

#include <cstring>

#include <cstdlib>

#include <cmath>

#include <iostream>

#include <iomanip>

const short N = 6;

double Lagrang(double X[N], double Fx[N], double _x)

{

double Wx = 1.0;

for (short i = 0; i < N; ++i)

Wx *= (_x - X[i]);

double result = 0.0;

for (short i = 0; i < N; ++i)

{

double dWx = 1.0;

for(short j = 0; j < N; ++j)

if (i!= j) dWx *= X[i] - X[j];

result += (Wx * Fx[i])/((_x - X[i]) * dWx);

}

return result;

}

void test()

{

double X[N] = {0.3, 0.4, 0.5, 0.6, 0.7, 0.8};

double Fx[N];

for (short i = 0; i < N; ++i)

Fx[i] = cos(X[i]);

std::cout << std::endl << "Cos_Lagr\t" << Lagrang(X, Fx, 0.55) << "\t" << cos(0.55);

for (short i = 0; i < N; ++i)

Fx[i] = sin(X[i]);

std::cout << std::endl << "Sin_Lagr\t" << Lagrang(X, Fx, 0.55) << "\t" << sin(0.55);

for (short i = 0; i < N; ++i)

Fx[i] = tan(X[i]);

std::cout << std::endl << "Tan_Lagr\t" << Lagrang(X, Fx, 0.55) << "\t" << tan(0.55);

}

int main(int argc, char** argv)

{

double X[6] = {0.41, 0.46, 0.52, 0.60, 0.65, 0.72};

double Fx[6] = {2.57418, 2.32513, 2.09336, 1.86203, 1.74926, 1.62098};

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

<< "Lagrang\t" << Lagrang(X, Fx, 0.537);

test();

std::system("pause");

return 0;

}

Вывод программы

Lagrang 2.037859651847294

Cos_Lagr 0.852524517903288 0.852524522059506

Sin_Lagr 0.522687226382460 0.522687228930659

Tan_Lagr 0.613108512374107 0.613105213288136

Тесты для основных тригонометрических функций подтверждают правильность работы алгоритма.