Estimated Bounds for Zeros of Polynomials from Traces of Graeffe Matrices

Ousmane Moussa Tessa; Maimouna Salou; Morou Amidou

doi:10.4236/alamt.2014.44019

Home > Journals > Physics & Mathematics > ALAMT

ALAMT> Vol.4 No.4, December 2014

Share This Article:

Open Access

Estimated Bounds for Zeros of Polynomials from Traces of Graeffe Matrices

Abstract Full-Text HTML XML

Download as PDF (Size:2529KB) PP. 210-215

DOI: 10.4236/alamt.2014.44019 3,417 Downloads 3,854 Views

Author(s) Leave a comment

Ousmane Moussa Tessa^1*, Maimouna Salou¹, Morou Amidou²

Affiliation(s)

¹Département de Mathématiques et d’informatique, Université A. Moumouni de Niamey, Niamey, Niger.
²Institut de Recherche sur l’Enseignement des Mathématiques, Université A. Moumouni de Niamey, Niamey, Niger.

ABSTRACT

In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant gain for the convergence towards the polynomials dominant zeros moduli.

KEYWORDS

Graeffe Matrices, Numerical Approximation of Eigenvalues, Dandelin-Graeffe’s Method, Bounds of Zeros of Polynomial

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Tessa, O. , Salou, M. and Amidou, M. (2014) Estimated Bounds for Zeros of Polynomials from Traces of Graeffe Matrices. Advances in Linear Algebra & Matrix Theory, 4, 210-215. doi: 10.4236/alamt.2014.44019.

References

[1]	Matthias, D. and Jurgen, K. (2007) On Bounds for the Zeros of Univariate Polynomials. Proceedings of World Academy of Science: Engineering & Technology, 20, 205.

[2]	Parodi, M. (1959) La Localisation des valeurs caractéristiques des Matrices et ses Applications. Gauthier-Villars, Paris.

[3]	Marden. M. (1949) The Geometry of the Zeros of a Polynomial in a Complex Variable. American Mathematical Society, New York. http://dx.doi.org/10.1090/surv/003

[4]	Dehmer, M. and Tsoy, Y.R. (2012) The Quality of Zero Bounds for Complex Polynomials. PLoS ONE, 7, e39537. http://dx.doi.org/10.1371/journal.pone.0039537

[5]	Linden, H. (1998) Bounds for the Zeros of Polynomials from Eigenvalues and Singular Values of Some Companion Matrices. Linear Algebra and Its Applications, 271, 41-82. http://dx.doi.org/10.1016/S0024-3795(97)00254-1

[6]	Mignotte, M. (1992) Mathematics for Computer Algebra. Springer Verlag, New York. http://dx.doi.org/10.1007/978-1-4613-9171-5

[7]	Mignotte, M. and Stefanescu, D. (2003) Linear Recurrent Sequences and Polynomial Roots. Journal of Symbolic Computation, 35, 637-649. http://dx.doi.org/10.1016/S0747-7171(03)00030-0

[8]	Kallol, P. and Santanu, B. (2012) On Numerical Radius of a Matrix and Estimation of Bounds for Zeros of a Polynomial. International Journal of Mathematics and Mathematical Sciences, 2012, Article ID: 129132.

[9]	Diouf, I. (2007) Méthode de Dandelin-Graeffe et Méthode de Baker. Thèses de Doctorat, Université Louis Pasteur de Strasbourg, Strasbourg.

[10]	Jacobson, N. (1985) Basic Algebra I. Fremann, New York.