POLYNOMIAL ROOT COMPUTATION BY MEANS OF THE LR ALGORITHM

By representing the $LR$ algorithm of Rutishauser and its variants in a polynomial setting, we derive numerical methods for approximating either all of the roots or a number $k$ of the roots of minimum modulus of a given polynomial $p(t)$ of degree $n$. These methods share the convergence properties of the $LR$ matrix iteration but, unlike it, they can be arranged to produce parallel and sequential algorithms which are highly efficient expecially in the case where $k<