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Isospectral flows on a class of finite-dimensional Jacobi matrices

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Title Isospectral flows on a class of finite-dimensional Jacobi matrices
 
Creator SUTTER, T
CHATTERJEE, D
RAMPONI, FA
LYGEROS, J
 
Subject Isospectral flow
Zero-diagonal Jacobi matrices
Block diagonal
EIGENVALUE
EQUATIONS
SYSTEMS
TODA
 
Description We present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes n x n zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e. features a right-hand side with a nested commutator of matrices and structurally resembles the double-bracket o.d.e. studied by R.W. Brockett in 1991. We prove that its solutions converge asymptotically, that the limit is block-diagonal, and above all, that the limit matrix is defined uniquely as follows: for n even, a block-diagonal matrix containing 2 x 2 blocks, such that the super-diagonal entries are sorted by strictly increasing absolute value. Furthermore, the off-diagonal entries in these 2 x 2 blocks have the same sign as the respective entries in the matrix employed as the initial condition. For n odd, there is one additional 1 x 1 block containing a zero that is the top left entry of the limit matrix. The results presented here extend some early work of Kac and van Moerbeke. (C) 2013 Elsevier B.V. All rights reserved.
 
Publisher ELSEVIER SCIENCE BV
 
Date 2014-10-14T17:15:56Z
2014-10-14T17:15:56Z
2013
 
Type Article
 
Identifier SYSTEMS & CONTROL LETTERS, 62(5)388-394
http://dx.doi.org/10.1016/j.sysconle.2013.02.004
http://dspace.library.iitb.ac.in/jspui/handle/100/14544
 
Language en