polyroot                package:base                R Documentation

_F_i_n_d _Z_e_r_o_s _o_f _a _R_e_a_l _o_r _C_o_m_p_l_e_x _P_o_l_y_n_o_m_i_a_l

_D_e_s_c_r_i_p_t_i_o_n:

     Find zeros of a real or complex polynomial.

_U_s_a_g_e:

     polyroot(z)

_A_r_g_u_m_e_n_t_s:

       z: the vector of polynomial coefficients in increasing order.

_D_e_t_a_i_l_s:

     A polynomial of degree n - 1,

              p(x) = z1 + z2 * x + ... + z[n] * x^(n-1)

     is given by its coefficient vector 'z[1:n]'. 'polyroot' returns
     the n-1 complex zeros of p(x) using the Jenkins-Traub algorithm.

     If the coefficient vector 'z' has zeroes for the highest powers,
     these are discarded.

     There is no maximum degree, but numerical stability may be an
     issue for all but low-degree polynomials.

_V_a_l_u_e:

     A complex vector of length n - 1, where n is the position of the
     largest non-zero element of 'z'.

_R_e_f_e_r_e_n_c_e_s:

     Jenkins and Traub (1972) TOMS Algorithm 419. _Comm. ACM_, *15*,
     97-99.

_S_e_e _A_l_s_o:

     'uniroot' for numerical root finding of arbitrary functions;
     'complex' and the 'zero' example in the demos directory.

_E_x_a_m_p_l_e_s:

     polyroot(c(1, 2, 1))
     round(polyroot(choose(8, 0:8)), 11) # guess what!
     for (n1 in 1:4) print(polyroot(1:n1), digits = 4)
     polyroot(c(1, 2, 1, 0, 0)) # same as the first