caa a22 4500 60619374X CHVBK 20210128100911.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00030-014-0276-z doi (NATIONALLICENCE)springer-10.1007/s00030-014-0276-z A Hessenberg-Jacobi isospectral flow [Elektronische Daten] [Alessandro Arsie, Christian Ebenbauer] In this paper we introduce an isospectral flow (Lax flow) that deforms real Hessenberg matrices to Jacobi matrices isospectrally. The Lax flow is given by $$\frac{dA}{dt} = [[A^T, A]_{du}, A],$$ d A d t = [ [ A T , A ] d u , A ] , where brackets indicate the usual matrix commutator, [A, B] := AB−BA, A T is the transpose of A and the matrix [A T , A] du is the matrix equal to [A T , A] along diagonal and upper triangular entries and zero below diagonal. We prove that if the initial condition A 0 is upper Hessenberg with simple spectrum and subdiagonal elements different from zero, then $${\lim_{t\rightarrow +\infty}A(t)}$$ lim t → + ∞ A ( t ) exists, it is a tridiagonal symmetric matrix isospectral to A 0 and it has the same sign pattern in the codiagonal elements as the initial condition A 0. Moreover we prove that the rate of convergence is exponential and that this system is the solution of an infinite horizon optimal control problem. Some simulations are provided to highlight some aspects of this nonlinear system and to provide possible extensions to its applicability. Springer Basel, 2014 Isospectral flow nationallicence Jacobi matrices nationallicence Omega-limit set nationallicence Differential equations on manifolds nationallicence Arsie Alessandro Department of Mathematics and Statistics, The University of Toledo, 43606, Toledo, OH, USA aut Ebenbauer Christian Institute for Systems Theory and Automatic Control, University of Stuttgart, 70550, Stuttgart, Baden-Württemberg, Germany aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/1(2015-02-01), 87-103 1021-9722 22:1<87 2015 22 30 https://doi.org/10.1007/s00030-014-0276-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-014-0276-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Arsie Alessandro Department of Mathematics and Statistics, The University of Toledo, 43606, Toledo, OH, USA aut NATIONALLICENCE 700 1- Ebenbauer Christian Institute for Systems Theory and Automatic Control, University of Stuttgart, 70550, Stuttgart, Baden-Württemberg, Germany aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/1(2015-02-01), 87-103 1021-9722 22:1<87 2015 22 30