void Polynom::laGuerre(dcmplx *xk, int iteraciones) {
dcmplx n = grado;
Polynom *pp = new Polynom(max, max);
pp->copyFrom(this);
pp->derivate();
Polynom *p2 = new Polynom(max, max);
p2->copyFrom(pp);
p2->derivate();
for (int i = 0; i < iteraciones; i++) {
dcmplx G = pp->evaluate(*xk) / evaluate(*xk);
dcmplx H = G * G -
p2->evaluate(*xk) / evaluate(*xk);
dcmplx a1 = G +
sqrt((n - (dcmplx) 1) * (n * H - G * G));
dcmplx a2 = G -
sqrt((n - (dcmplx) 1) * (n * H - G * G));
dcmplx a;
if(abs(a1) > abs(a2))
a = n / a1;
else
a = n / a2;
*xk = *xk - a;
if(evaluate(*xk) == dcmplx(0))
break;
}
}
void Polynom::roots(dcmplx *roots)
{
Polynom *temporal = new Polynom(grado, max);
temporal->copyFrom(this);
for(int i = 0; i < grado; i++)
{
dcmplx *xk = new dcmplx(0, 0);
temporal->laGuerre(xk, 50);
if(xk->imag() >= 1e-6)
{
Polynom *divisible = new Polynom(2, 3);
divisible->coef[0] = xk->real() * xk->real()
+ xk->imag() * xk->imag();
divisible->coef[1] = -2 * xk->real();
divisible->coef[2] = 1;
*temporal /= divisible;
roots[i] = *xk;
dcmplx *xk1 = new dcmplx(xk->real(), xk->imag());
delete divisible;
roots[++i] = *xk1;
}
else
{
Polynom *divisible = new Polynom(1, 2);
divisible->coef[0] = -(xk->real());
divisible->coef[1] = 1;
*temporal /= divisible;
delete divisible;
dcmplx *xk1 = new dcmplx(xk->real(), 0);
delete xk;
roots[i] = *xk1;
}
}
}