Linear recurrent sequences and polynomial roots

  • Authors:

  • Maurice Mignotte;Doru Ştefánescu

  • Affiliations:

  • Université Louis Pasteur, 7, Rue Descartes, 67084, Strasbourg, France;Faculty of Physics, Department of Mathematics, University of Bucharest, PO Box 39-D5, Bucharest 39, Romania

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2003

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Abstract

We consider the problem of the determination of the largest modulus of a root of a complex polynomial P. We obtain lower and upper bounds using properties of appropriate linear recurrent sequences associated with P. This allows giving the absolute value of a dominant root as the limit as in Bernoulli's process. We finally discuss a rule of Jacobi in his refinement of Bernoulli's method. Relevant examples are obtained through pari and maple procedures.