

polyroot {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 decreas-
          ing 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]'.  `poly-
     root' returns the n-1 complex zeros of p(x) using the
     Jenkins-Traub algorithm.

_V_a_l_u_e_:

     A complex vector of length n - 1, where n is
     `length(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 func-
     tions; `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)

