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@article{697292, author = {Hilscher, Roman and Zeidan, Vera}, article_location = {USA}, article_number = {2-3}, keywords = {Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Coupled interval; Conjugate interval; Conjoined basis}, language = {eng}, issn = {0024-3795}, journal = {Linear Algebra and its Applications}, title = {Coupled intervals for discrete symplectic systems}, volume = {419}, year = {2006} }
TY - JOUR ID - 697292 AU - Hilscher, Roman - Zeidan, Vera PY - 2006 TI - Coupled intervals for discrete symplectic systems JF - Linear Algebra and its Applications VL - 419 IS - 2-3 SP - 750-764 EP - 750-764 PB - Elsevier Science SN - 00243795 KW - Discrete symplectic system KW - Quadratic functional KW - Nonnegativity KW - Positivity KW - Coupled interval KW - Conjugate interval KW - Conjoined basis N2 - 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. ER -
HILSCHER, Roman and Vera ZEIDAN. Coupled intervals for discrete symplectic systems. \textit{Linear Algebra and its Applications}. USA: Elsevier Science, 2006, vol.~419, 2-3, p.~750-764. ISSN~0024-3795.
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