- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, April 20, 2015 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Dr. Antonio Cicone – L'Aquila, Italy
- Organizer
- Haomin Zhou
Given a finite set of matrices F, the Markovian Joint Spectral
Radius represents the maximal rate of growth of products of matrices in
F when the matrices are multiplied each other following some Markovian law.
This quantity is important, for instance, in the study of the so called
zero stability of variable stepsize BDF methods for the numerical
integration of ordinary differential equations.
Recently Kozyakin, based on a work by Dai, showed that, given a set F of
N matrices of dimension d and a graph G, which represents the admissible
products, it is possibile to compute the Markovian Joint Spectral Radius
of the couple (F,G) as the classical Joint Spectral Radius of a new set
of N matrices of dimension N*d, which are produced as a particular
lifting of the matrices in F. Clearly by this approach the exact
evaluation or the simple approximation of the Markovian Joint Spectral
Radius becomes a challenge even for reasonably small values of N and d.
In this talk we briefly review the theory of the Joint Spectral Radius,
and we introduce the Markovian Joint Spectral Radius. Furthermore we
address the question whether it is possible to reduce the exact
calculation computational complexity of the Markovian Joint Spectral
Radius. We show that the problem can be recast as the computation of N
polytope norms in dimension d. We conclude the presentation with some
numerical examples.
This talk is based on a joint work with Nicola Guglielmi from the
University of L'Aquila, Italy, and Vladimir Yu. Protasov from the Moscow
State University, Russia.