Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
If the system semigroup of a control system is a roup, the system has the partition property, i.e., the reachable sets form a disjoint partition in the state space. The converse is ot true in general. In this work we give sufficient conditions for le partition property for a family of discrete-time control systems on homogeneous spaces. We apply our results to Inverse Iteration systems on flag manifolds, which are closely related to numerical aIgorithms.
Czasopismo
Rocznik
Tom
Strony
863--871
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Universitat Würzburg, Institut für Mathematik, 97074 Würzburg, Germany
Bibliografia
- AMMAR, G.S. and MARTIN, C.F. (1986) The geometry of matrix eigenvalue methods. Acta Applicandae Mathematicae 5, 239-278.
- BATTERSON, S. and SMILLIE, J. (1989) The dynamics of Rayleigh quotient iteration. SIAM J. Numer. Anal. 26, 624-636.
- BATTERSON, S. and SMILLIE, J. (1990) Rayleigh quotient iteration for non-symmetric matrices Math, of Computation 55 (191), 169-178.
- FUHRMANN, P.A. (1996) A Polynomial Approach to Linear Algebra. Springer Publ., New York.
- HELMKE, U. and FUHRMANN, P.A. (2000) Controllability of matrix eigenvalue algorithms: the inverse power method. Systems and Control Letters 41, 57-66.
- HELMKE, U. and JORDAN, J. (2002) Numerics versus control. Mathematical Systems Theory in Biology, Communications, Computations and Finance 134, IMA Conference, 223-236.
- HELMKE, U. and WIRTH, F. (2001) On controllability of the real shifted inverse power iteration. Systems and Control Letters 43, 9-23.
- MITTENHUBER, D. (2001) Transitive semigroup actions and controllability of systems on Lie groups: A solvable and a semisimple problem. Habilitationsschrift. Technical University of Darmstadt.
- SAN MARTIN, L.A.B. (1998) Homogeneous spaces admitting transitive semigroups. Journal of Lie Theory 8, 111-128.
- SONTAG, E.D. (1998) Mathematical Control Theory: Deterministic Finite Dimensional Systems. Texts in Applied Mathematics 6, 2nd Edition. Springer Verlag, New York.
- SHUB, M. and VASQUEZ, T. (1987) Some linearly induced Morse-Smale systems, the QR algorithm and the Toda lattice. In: L. Keen, ed., The Legacy of Sonya Kovalevskaya, Contemporary Mathematics, 64, A.M.S., 181-194.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0014-0025