Graeffe's root squaring method: its solvability conditions, software modification and extension

Abstract

Gruetl"\;'s method determi L1CS all Ihe roots of univariate polynomials both real and complex, repeated ill1dnon-repeated simultaneollsly.ln lhi~ thesis, it I, ~aid that this ~la\Cmcnt is no! universally [me, It is shown tilat the method is valid if the algebraic cq\lation~ ~alisfy the condition~, (i) equations with zero coellidcnt lll\l~l have at leasl one pair of equidistant llon-~cro coeJTicient from the /,cro coefficient. (ii) any transformed equation of a given ~quation with n01\-7£1'O coefficient may have zero coefficients but these new cocffici~nt5 must satisfy (i). (iii) all the coel1icicnts ofnlln-lincar equation must nol be unity. GRAEFFE.BAS program 19] ha, been modified in these light and has been extended for nol ~()Ivabje equations.