منابع مشابه
Tangent Graeffe iteration
Graeffe iteration was the choice algorithm for solving univariate polynomials in the XIX-th and early XX-th century. In this paper, a new variation of Graeffe iteration is given, suitable to IEEE floating-point arithmetics of modern digital computers. We prove that under a certain generic assumption the proposed algorithm converges. We also estimate the error after N iterations and the running ...
متن کاملOn the Geometry of Graeffe Iteration
A new version of the Graeffe’s algorithms for finding all the roots of univariate complex polynomials is proposed. It is obtained from the classical algorithm by a process analogous to renormalization of dynamical systems. This iteration is called Renormalized Graeffe Iteration. It is globally convergent, with probability 1. All quantities involved in the computation are bounded, once the initi...
متن کاملThe Graeffe Process as Applied to Power Series
Of the many methods which have been proposed for solving algebraic equations the most practical one, where complex roots are concerned, is the well known "root-squaring" method usually referred to as the Graeffe1 process. Nearly all accounts of the method show by examples how all the roots of an equation may be found by first finding all the absolute values of the roots, and later by various de...
متن کاملThe Graeffe Process as Applied to Power Series
Of the many methods which have been proposed for solving algebraic equations the most practical one, where complex roots are concerned, is the well known "root-squaring" method usually referred to as the Graeffe1 process. Nearly all accounts of the method show by examples how all the roots of an equation may be found by first finding all the absolute values of the roots, and later by various de...
متن کاملTangent Algebras
We study the Zariski tangent cone TX π −→ X to an affine variety X and the closure TX of π−1(Reg(X)) in TX . We focus on the comparison between TX and TX , giving sufficient conditions on X in order that TX = TX . One aspect of the results is to understand when this equality takes place in the presence of the reducedness of the Zariski tangent cone. Our other interest is to consider conditions ...
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ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2001
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s002110100278