Computing the zeros of quaternion polynomials

A method is developed to compute the zeros of a quaternion polynomial with all terms of the form q(k) X-k. This method is based essentially in Niven's algorithm [1], which consists of dividing the polynomial by a characterist ic polynomial associated to a zero. The information about the trace and the norm of the zero is obtained by an original idea which requires the compan ion matrix associated to the polynomial. The companion matrix is represente d by a matrix with complex entries. Three numerical examples using Mathemat ica 2.2 version are given. (C) 2001 Elsevier Science Ltd. All rights reserv ed.