Comptes Rendus
Numerical analysis
Improvement of Pellet's theorem for scalar and matrix polynomials
Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 859-863.

We improve Pellet's theorem for both scalar and matrix polynomials by using polynomial multipliers.

Nous améliorons le théorème de Pellet pour les polynômes scalaires et matriciels en utilisant des multiplicateurs polynomiaux.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.04.006

Aaron Melman 1

1 Department of Applied Mathematics, School of Engineering, Santa Clara University, Santa Clara, CA 95053, USA
@article{CRMATH_2016__354_8_859_0,
     author = {Aaron Melman},
     title = {Improvement of {Pellet's} theorem for scalar and matrix polynomials},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {859--863},
     publisher = {Elsevier},
     volume = {354},
     number = {8},
     year = {2016},
     doi = {10.1016/j.crma.2016.04.006},
     language = {en},
}
TY  - JOUR
AU  - Aaron Melman
TI  - Improvement of Pellet's theorem for scalar and matrix polynomials
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 859
EP  - 863
VL  - 354
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2016.04.006
LA  - en
ID  - CRMATH_2016__354_8_859_0
ER  - 
%0 Journal Article
%A Aaron Melman
%T Improvement of Pellet's theorem for scalar and matrix polynomials
%J Comptes Rendus. Mathématique
%D 2016
%P 859-863
%V 354
%N 8
%I Elsevier
%R 10.1016/j.crma.2016.04.006
%G en
%F CRMATH_2016__354_8_859_0
Aaron Melman. Improvement of Pellet's theorem for scalar and matrix polynomials. Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 859-863. doi : 10.1016/j.crma.2016.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.04.006/

[1] D.A. Bini; V. Noferini; M. Sharify Locating the eigenvalues of matrix polynomials, SIAM J. Matrix Anal. Appl., Volume 34 (2013), pp. 1708-1727

[2] A.L. Cauchy, Exercices de mathématiques, Quatrième année (Œuvres complètes, Série 2), Volume Tome 9, de Bure frères, Paris (1829), pp. 65-128 (Also in:, 1891, Gauthier-Villars et fils, Paris, pp. 86-161)

[3] N.J. Higham; F. Tisseur Bounds for eigenvalues of matrix polynomials, Linear Algebra Appl., Volume 358 (2003), pp. 5-22

[4] R.A. Horn; C.R. Johnson Matrix Analysis, Cambridge University Press, Cambridge, UK, 2013

[5] M. Marden Geometry of Polynomials, Mathematical Surveys, vol. 3, American Mathematical Society, Providence, RI, USA, 1966

[6] A. Melman Generalization and variations of Pellet's theorem for matrix polynomials, Linear Algebra Appl., Volume 439 (2013), pp. 1550-1567

[7] A. Melman Implementation of Pellet's theorem, Numer. Algorithms, Volume 65 (2014), pp. 293-304

[8] M.A. Pellet Sur un mode de séparation des racines des équations et la formule de Lagrange, Bull. Sci. Math., Volume 5 (1881), pp. 393-395

[9] Q.I. Rahman; G. Schmeisser Analytic Theory of Polynomials, London Mathematical Society Monographs. New Series, vol. 26, The Clarendon Press, Oxford University Press, Oxford, UK, 2002

Cited by Sources:

Comments - Politique