Newton-Raphson法求解非线性方程复根

//用Newton-Raphson法求解非线性方程复根

#include <iostream>

#include <math.h>

#include <process.h>

using namespace std;

class raphson

{

private:

int iteration, flag;

double eps, error1, error2, f_u, f_v, f_u_alpha, f_u_beta;

double alpha_new, alpha_old, beta_new, beta_old;

double term1, term2, term3, term4, term5;

public:

raphson()

{

iteration = 0;

flag = 1;

}

void solution();

double u(double a1, double b1)

{

f_u = a1 * a1 - b1 * b1 - 2 * a1 + 2;

return f_u;

}

double v(double a2, double b2)

{

f_v = 2 * a2 * b2 - 2 * b2;

return f_v;

}

double u_alpha(double a3, double b3)

{

f_u_alpha = 2 * a3 - 2;

return f_u_alpha;

}

double u_beta(double a4, double b4)

{

f_u_beta = -2 * b4;

return f_u_beta;

}

};

void main()

{

raphson nonlinear;

nonlinear.solution();

}

void raphson::solution()

{

cout << "\n输入alpha初值：";

cin >> alpha_old;

cout << "\n输入beta初值：";

cin >> beta_old;

cout << "\n输入公差：";

cin >> eps;

do

{

iteration++;

term1 = u(alpha_old, beta_old);

term2 = v(alpha_old, beta_old);

term3 = u_alpha(alpha_old, beta_old);

term4 = u_beta(alpha_old, beta_old);

term5 = term3 * term3 + term4 * term4;

if (term5 == 0)

{

cout << "\n遇到了被0除，程序中断..." << endl;

exit(0);

}

alpha_new = alpha_old + (term2 * term4 - term1 * term3) / term5;

beta_new = beta_old - (term2 * term3 + term1 * term4) / term5;

error1 = fabs(term1);

error2 = fabs(term2);

if ((error1 < eps) && (error2 < eps))

{

flag = 0;

}

alpha_old = alpha_new;

beta_old = beta_new;

}while (flag == 1);

cout << "\n解是：" << endl;

cout << "\n实部：" << alpha_new << endl;

cout << "\n虚部：" << beta_new << endl;

cout << "\n在第" << iteration << "次迭代收敛。" << endl;

}