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.
Accepted:
Published online:
Aaron Melman 1
@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}, }
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] Locating the eigenvalues of matrix polynomials, SIAM J. Matrix Anal. Appl., Volume 34 (2013), pp. 1708-1727
[2] , 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] Bounds for eigenvalues of matrix polynomials, Linear Algebra Appl., Volume 358 (2003), pp. 5-22
[4] Matrix Analysis, Cambridge University Press, Cambridge, UK, 2013
[5] Geometry of Polynomials, Mathematical Surveys, vol. 3, American Mathematical Society, Providence, RI, USA, 1966
[6] Generalization and variations of Pellet's theorem for matrix polynomials, Linear Algebra Appl., Volume 439 (2013), pp. 1550-1567
[7] Implementation of Pellet's theorem, Numer. Algorithms, Volume 65 (2014), pp. 293-304
[8] Sur un mode de séparation des racines des équations et la formule de Lagrange, Bull. Sci. Math., Volume 5 (1881), pp. 393-395
[9] Analytic Theory of Polynomials, London Mathematical Society Monographs. New Series, vol. 26, The Clarendon Press, Oxford University Press, Oxford, UK, 2002
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