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2007 | 17 | 2 | 173-178
Tytuł artykułu

Falseness of the finiteness property of the spectral subradius

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive because we do not show any explicit value of α that has described property. The problem of finding such values is still open.
Słowa kluczowe
Rocznik
Tom
17
Numer
2
Strony
173-178
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-01-19
poprawiono
2006-11-02
(nieznana)
2007-02-23
Twórcy
autor
  • Department of Automatic Control, Silesian University of Technology, ul. Akademicka 17, 44–101 Gliwice, Poland
autor
  • Polish-Japanese Institute of Information Technology, ul. Aleja Legionów 2, 41–902 Bytom, Poland
Bibliografia
  • Elsner L. (1995): The generalized spectral radius theorem: An analytic-geometric proof. - Linear Algebra Appl., Vol.220,pp.151-159.
  • Blondel V.D., Theys J. and Vladimirov A.A. (2003): An elementary counter example to the finitness conjecture. - SIAM J. Matrix Anal. Appl., Vol.24, No.4, pp.963-970.
  • Czornik A. (2005): On the generalized spectral subradius. -Linear Algebra Appl., Vol.407, pp.242-248.
  • Horn R.A. and Johnson C.R. (1991): Topics in Matrix Analysis. - Cambridge, UK: Cambridge University Press.
  • Horn R.A. and Johnson C.R. (1985): Matrix Analysis. -Cambridge, UK: Cambridge University Press.
  • Lagarias J.C. and Wang Y. (1995): The finiteness conjecture for the generalized spectral radius of a set of matrices. - Linear Algebra Appl., Vol.214, pp.17-42.
  • Tsitsiklis J. and Blondel V. (1997): The Lyapunov exponent and joint spectral radius of pairs of matrices are hard - when not impossible to compute and to approximate. -Math. Contr. Signals Syst., Vol.10, pp.31-40
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv17i2p173bwm
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