Symplectic difference systems: variable stepsize discretization
and discrete quadratic functionals

J 2003

Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals

HILSCHER, Roman a Vera ZEIDAN

Základní údaje

Originální název

Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals

Autoři

HILSCHER, Roman a Vera ZEIDAN

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

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/03:00008171

Organizační jednotka

Přírodovědecká fakulta

UT WoS

000182997900007

Klíčová slova anglicky

symplectic difference system; discrete quadratic functional; variable stepsize; linear Hamiltonian difference system; conjugate interval; conjoined basis; Riccati difference equation; variable state endpoints

Štítky

conjoined basis, conjugate interval, discrete quadratic functional, linear Hamiltonian difference system, Riccati difference equation, Symplectic difference system, variable state endpoints, variable stepsize

Změněno: 26. 6. 2009 07:44, prof. RNDr. Roman Šimon Hilscher, DSc.

Anotace

V originále

Discrete quadratic functionals with variable endpoints for variable stepsize symplectic difference systems are considered. A comprehensive study is presented for characterizing the positivity of such functionals in terms of conjugate intervals, conjoined bases, and implicit and explicit Riccati equations with various forms of boundary conditions. Moreover, necessary conditions for the nonnegativity of these functionals are obtained in terms of the above notions. Furthermore, we show that a variable stepsize discretization of a continuous-time nonlinear control problem leads to a discrete linear quadratic problem and a Hamiltonian difference system, which are special cases of their symplectic counterparts.

Návaznosti

GA201/01/0079, projekt VaV

Název: Kvalitativní teorie řešení diferenčních rovnic

Investor: Grantová agentura ČR, Kvalitativní teorie řešení diferenčních rovnic

Citovat

HILSCHER, Roman a Vera ZEIDAN. Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals. Linear Algebra and its Applications. USA: Elsevier Science, 2003, roč. 367, č. 1, s. 67-104. ISSN 0024-3795.

@article{488397,
   author = {Hilscher, Roman and Zeidan, Vera},
   article_location = {USA},
   article_number = {1},
   keywords = {symplectic difference system; discrete quadratic functional; variable stepsize; linear Hamiltonian difference system; conjugate interval; conjoined basis; Riccati difference equation; variable state endpoints},
   language = {eng},
   issn = {0024-3795},
   journal = {Linear Algebra and its Applications},
   title = {Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals},
   volume = {367},
   year = {2003}
}

TY  - JOUR
ID  - 488397
AU  - Hilscher, Roman - Zeidan, Vera
PY  - 2003
TI  - Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals
JF  - Linear Algebra and its Applications
VL  - 367
IS  - 1
SP  - 67-104
EP  - 67-104
PB  - Elsevier Science
SN  - 00243795
KW  - symplectic difference system
KW  - discrete quadratic functional
KW  - variable stepsize
KW  - linear Hamiltonian difference system
KW  - conjugate interval
KW  - conjoined basis
KW  - Riccati difference equation
KW  - variable state endpoints
N2  - Discrete quadratic functionals with variable endpoints for variable stepsize symplectic difference systems are considered. A comprehensive study is presented for characterizing the positivity of such functionals in terms of conjugate intervals, conjoined bases, and implicit and explicit Riccati equations with various forms of boundary conditions. Moreover, necessary conditions for the nonnegativity of these functionals are obtained in terms of the above notions. Furthermore, we show that a variable stepsize discretization of a continuous-time nonlinear control problem leads to a discrete linear quadratic problem and a Hamiltonian difference system, which are special cases of their symplectic counterparts.
ER  -

HILSCHER, Roman a Vera ZEIDAN. Symplectic difference systems: variable stepsize discretization and discrete quadratic functionals. \textit{Linear Algebra and its Applications}. USA: Elsevier Science, 2003, roč.~367, č.~1, s.~67-104. ISSN~0024-3795.

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