Coupled intervals for discrete symplectic systems
| Authors | |
|---|---|
| Year of publication | 2006 |
| Type | Article in Periodical |
| Magazine / Source | Linear Algebra and its Applications |
| MU Faculty or unit | |
| Citation | |
| 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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