POLYNOMIAL ROOT COMPUTATION BY MEANS OF THE LR ALGORITHM

Gemignani, Luca (1996) POLYNOMIAL ROOT COMPUTATION BY MEANS OF THE LR ALGORITHM. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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Abstract

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 $k<<n$.

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