Comptes Rendus
no. 8
Numerical analysis
Improvement of Pellet's theorem for scalar and matrix polynomials
[Amélioration du théorème de Pellet pour polynômes scalaires et matriciels]

Présenté par : Olivier Pironneau

Aaron Melman1
1 Department of Applied Mathematics, School of Engineering, Santa Clara University, Santa Clara, CA 95053, USA
Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 859-863.

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

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

Reçu le :
Accepté le :
Publié le :
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 
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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/

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[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

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  • A. Melman Matrices whose eigenvalues are those of a quadratic matrix polynomial, Linear Algebra and its Applications, Volume 676 (2023), p. 131 | DOI:10.1016/j.laa.2023.06.025
  • Aaron Melman Polynomial eigenvalue estimation: numerical radii versus norms, Linear and Multilinear Algebra, Volume 70 (2022) no. 22, p. 7656 | DOI:10.1080/03081087.2021.2003286
  • A. Melman Directional bounds for polynomial zeros and eigenvalues, Journal of Mathematical Analysis and Applications, Volume 482 (2020) no. 2, p. 123571 | DOI:10.1016/j.jmaa.2019.123571
  • A. Melman Refinement of Pellet radii for matrix polynomials, Linear and Multilinear Algebra, Volume 68 (2020) no. 11, p. 2185 | DOI:10.1080/03081087.2019.1573212
  • A. Melman An alternative proof of Pellet’s theorem for matrix polynomials, Linear and Multilinear Algebra, Volume 66 (2018) no. 4, p. 785 | DOI:10.1080/03081087.2017.1322549

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