Publication details

Coupled intervals for discrete symplectic systems

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Year of publication 2006
Type Article in Periodical
Magazine / Source Linear Algebra and its Applications
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Coupled interval; Conjugate interval; Conjoined basis
Description In this paper we introduce (strict) coupled intervals for discrete symplectic systems and characterize in terms of the nonexistence of such coupled intervals the definiteness of the associated discrete quadratic functional with variable endpoints. This (strict) coupled interval notion generalizes (i) the (strict) conjugate interval notion known for discrete variational problems with fixed right endpoint, and (ii) the (strict) coupled interval notion known for the special case of linear Hamiltonian systems. The applicability of this theory of coupled intervals is clearly illustrated by a numerical example emanating from a nonlinear discrete control problem.
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