| DOŠLÝ, Ondřej, Roman HILSCHER a Vera ZEIDAN. Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. Linear Algebra and its Applications. USA: Elsevier Science, 2003, roč. 375, 1.12.2003, s. 21-44. ISSN 0024-3795. |
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@article{489754,
author = {Došlý, Ondřej and Hilscher, Roman and Zeidan, Vera},
article_location = {USA},
article_number = {1.12.2003},
keywords = {Symplectic difference system; Discrete quadratic functional; Nonnegativity; Positivity; Focal point; Conjoined basis; Riccati difference equation; Linear Hamiltonian difference system},
language = {eng},
issn = {0024-3795},
journal = {Linear Algebra and its Applications},
title = {Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems},
volume = {375},
year = {2003}
}
TY - JOUR
ID - 489754
AU - Došlý, Ondřej - Hilscher, Roman - Zeidan, Vera
PY - 2003
TI - Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems
JF - Linear Algebra and its Applications
VL - 375
IS - 1.12.2003
SP - 21-44
EP - 21-44
PB - Elsevier Science
SN - 00243795
KW - Symplectic difference system
KW - Discrete quadratic functional
KW - Nonnegativity
KW - Positivity
KW - Focal point
KW - Conjoined basis
KW - Riccati difference equation
KW - Linear Hamiltonian difference system
N2 - We study the nonnegativity of quadratic functionals with separable endpoints which are related to the discrete symplectic system (S). In particular, we characterize the nonnegativity of these functionals in terms of (i) the focal points of the natural conjoined basis of (S) and (ii) the solvability of an implicit Riccati equation associated with (S). This result is closely related to the kernel condition for the natural conjoined basis of (S). We treat the situation when this kernel condition is possibly violated at a certain index. To accomplish this goal, we derive a new characterization of the set of admissible pairs (sequences) that does not require the validity of the above mentioned kernel condition. Finally, we generalize our results to the variable stepsize case.
ER -
DOŠLÝ, Ondřej, Roman HILSCHER a Vera ZEIDAN. Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems. \textit{Linear Algebra and its Applications}. USA: Elsevier Science, 2003, roč.~375, 1.12.2003, s.~21-44. ISSN~0024-3795.
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