Accurate computation of the zeros of the generalized Bessel polynomials

A general method for approximating polynomial solutions of second-order lin ear homogeneous differential equations with polynomial coefficients is appl ied to the case of the families of differential equations defining the gene ralized Bessel polynomials, and an algorithm is derived for simultaneously finding their zeros. Then a comparison with several alternative algorithms is carried out. It shows that the computational problem of approximating th e zeros of the generalized Bessel polynomials is not an easy matter at all and that the only algorithm able to give an accurate solution seems to be t he one presented in this paper. Mathematics Subject Classification (1991): 65F15, 65F30, 65H20.