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Abstract
In this paper we study the convergence of Halley’s method as a method for finding all zeros of a polynomial simultaneously. We present two types of local convergence theorems as well as a semilocal convergence theorem for Halley’s method for simultaneous computation of polynomial zeros.
Keywords : Halley’s method; polynomial zeros; simultaneous methods; local convergence; semilocal convergence; error estimates
Received: 2013-6-1
Accepted: 2014-6-2
Published Online: 2015-12-8
Published in Print: 2015-12-1
© 2015 by Walter de Gruyter Berlin/Boston
