Comptes Rendus
no. 6
Analyse numérique
Sur la distance à l'instabilité de polynômes matriciels quadratiques
[On the distance to instability of quadratic matrix polynomials]

Presented by: le Comité de rédaction

Alexander Malyshev1; Miloud Sadkane2
1 University of Bergen, Department of Mathematics, Postbox 7803, 5020 Bergen, Norway
2 Université de Brest, CNRS – UMR 6205, Mathématiques, 6, avenue Victor-Le-Gorgeu, 29238 Brest cedex 3, France
Comptes Rendus. Mathématique, Volume 357 (2019) no. 6, pp. 571-575.

A bisection method is developed for computing the distance to instability of quadratic matrix polynomials. The computation takes rounding errors into account.

Nous développons une méthode de type bissection pour calculer la distance à l'instabilité de polynômes matriciels quadratiques. Le calcul prend en compte les erreurs d'arrondi.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.06.007

Alexander Malyshev 1; Miloud Sadkane 2

1 University of Bergen, Department of Mathematics, Postbox 7803, 5020 Bergen, Norway
2 Université de Brest, CNRS – UMR 6205, Mathématiques, 6, avenue Victor-Le-Gorgeu, 29238 Brest cedex 3, France 
@article{CRMATH_2019__357_6_571_0,
     author = {Alexander Malyshev and Miloud Sadkane},
     title = {Sur la distance \`a l'instabilit\'e de polyn\^omes matriciels quadratiques},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {571--575},
     publisher = {Elsevier},
     volume = {357},
     number = {6},
     year = {2019},
     doi = {10.1016/j.crma.2019.06.007},
     language = {fr},
}
TY  - JOUR
AU  - Alexander Malyshev
AU  - Miloud Sadkane
TI  - Sur la distance à l'instabilité de polynômes matriciels quadratiques
JO  - Comptes Rendus. Mathématique
PY  - 2019
SP  - 571
EP  - 575
VL  - 357
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2019.06.007
LA  - fr
ID  - CRMATH_2019__357_6_571_0
ER  - 
%0 Journal Article
%A Alexander Malyshev
%A Miloud Sadkane
%T Sur la distance à l'instabilité de polynômes matriciels quadratiques
%J Comptes Rendus. Mathématique
%D 2019
%P 571-575
%V 357
%N 6
%I Elsevier
%R 10.1016/j.crma.2019.06.007
%G fr
%F CRMATH_2019__357_6_571_0
Alexander Malyshev; Miloud Sadkane. Sur la distance à l'instabilité de polynômes matriciels quadratiques. Comptes Rendus. Mathématique, Volume 357 (2019) no. 6, pp. 571-575. doi : 10.1016/j.crma.2019.06.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.06.007/

[1] Y. Genin; R. Stefan; P. Van Dooren Real and complex stability radii of polynomial matrices, Linear Algebra Appl., Volume 351–352 (2002), pp. 381-410

[2] G.H. Golub; C.F. Van Loan Matrix Computations, The John Hopkins University Press, Baltimore, MD, USA, 2013

[3] S. Hammarling; C.R. Munro; F. Tisseur An algorithm for the complete solution of quadratic eigenvalue problems, ACM Trans. Math. Softw., Volume 39 (2013)

[4] D.S. Mackey; N. Mackey; C. Mehl; V. Mehrmann Numerical methods for palindromic eigenvalue problems: computing the anti-triangular Schur form, Numer. Linear Algebra Appl., Volume 16 (2009), pp. 63-86

[5] A. Malyshev; M. Sadkane On the computation of the distance to quadratic matrix polynomials that are singular at some points on the unit circle, Electron. Trans. Numer. Anal., Volume 42 (2014), pp. 165-176

[6] C.B. Moler; G.W. Stewart An algorithm for generalized matrix eigenvalue problems, SIAM J. Numer. Anal., Volume 10 (1973), pp. 241-256

[7] B.N. Parlett The Symmetric Eigenvalue Problem, SIAM, Philadelphia, PA, USA, 1998

Cited by Sources:

Comments - Policy