Tangent Graeffe Iteration

Details Tangent Graeffe Iteration Tangent Graeffe Iteration

1999-08-27

arxiv.org/abs/math/9908150v1

Numerische Mathematik, Volume 89, Number 4 / October, 2001.

Mathematics

Numerical Analysis

Scientific paper

10.1007/s002110100278

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 cost. The main ideas from which this algorithm is built are: classical Graeffe iteration and Newton Diagrams, changes of scale (renormalization), and replacement of a difference technique by a differentiation one. The algorithm was implemented successfully and a number of numerical experiments are displayed.

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