Nonnegativity of discrete quadratic functionals corresponding
to symplectic difference systems

J 2003

Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems

DOŠLÝ, Ondřej, Roman HILSCHER a Vera ZEIDAN

Základní údaje

Originální název

Nonnegativity of discrete quadratic functionals corresponding to symplectic difference systems

Autoři

DOŠLÝ, Ondřej (203 Česká republika), Roman HILSCHER (203 Česká republika, garant) a Vera ZEIDAN (840 Spojené státy)

Vydání

Linear Algebra and its Applications, USA, Elsevier Science, 2003, 0024-3795

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.656

Kód RIV

RIV/00216224:14310/03:00008259

Organizační jednotka

Přírodovědecká fakulta

UT WoS

000186340700003

Klíčová slova anglicky

Symplectic difference system; Discrete quadratic functional; Nonnegativity; Positivity; Focal point; Conjoined basis; Riccati difference equation; Linear Hamiltonian difference system

Štítky

conjoined basis, discrete quadratic functional, focal point, linear Hamiltonian difference system, Nonnegativity, Positivity, Riccati difference equation, Symplectic difference system

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 26. 6. 2009 07:17, prof. RNDr. Roman Šimon Hilscher, DSc.

Anotace

V originále

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.

Návaznosti

GA201/01/0079, projekt VaV

Název: Kvalitativní teorie řešení diferenčních rovnic

Investor: Grantová agentura ČR, Kvalitativní teorie řešení diferenčních rovnic

MSM 143100001, záměr

Název: Funkcionální diferenciální rovnice a matematicko-statistické modely

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Funkcionální diferenciální rovnice a matematicko-statistické modely

Citovat

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.

@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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