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An algorithm for finding extremal polytope norms of matrix families

GUGLIELMI N.
•
ZENNARO, MARINO
2008
  • journal article

Periodico
LINEAR ALGEBRA AND ITS APPLICATIONS
Abstract
In this paper the problem of the computation of the joint spectral radius of a finite set of matrices is considered. We present an algorithm which, under some suitable assumptions, is able to check if a certain product in the multiplicative semigroup is spectrum maximizing. The algorithm proceeds by attempting to construct a suitable extremal norm for the family, namely a complex polytope norm. As examples for testing our technique, we first consider the set of two 2-dimensional matrices recently analyzed by Blondel, Nesterov and Theys to disprove the finiteness conjecture, and then a set of 3-dimensional matrices arising in the zero-stability analysis of the 4-step BDF formula for ordinary differential equations.
DOI
10.1016/j.laa.2007.07.009
WOS
WOS:000255431900003
Archivio
http://hdl.handle.net/11368/1752391
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-40849114591
Diritti
metadata only access
Soggetti
  • joint spectral radiu

  • balanced complex poly...

  • complex polytope norm...

Web of Science© citazioni
38
Data di acquisizione
Mar 18, 2024
Visualizzazioni
4
Data di acquisizione
Apr 19, 2024
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