Nonnegativity of a discrete quadratic functional in terms of
the (strengthened) Legendre and Jacobi conditions

J 2003

Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions

HILSCHER, Roman a Vera ZEIDAN

Základní údaje

Originální název

Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions

Autoři

HILSCHER, Roman a Vera ZEIDAN

Vydání

Computers & mathematics with applications, New York, Pergamon Press, 2003, 0097-4943

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

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/03:00008168

Organizační jednotka

Přírodovědecká fakulta

UT WoS

000183453300042

Klíčová slova anglicky

discrete quadratic functional; Legendre condition; Jacobi difference equation; conjugate interval; discrete calculus of variations

Štítky

conjugate interval, discrete calculus of variations, discrete quadratic functional, Jacobi difference equation, Legendre condition

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

Anotace

V originále

This paper contains a complete characterization of the nonnegativity of a discrete quadratic functional with one endpoint allowed to vary. In particular, we derive the exact form and explain the role of the (strengthened) Legendre condition in the discrete calculus of variations. Under this condition, the nonnegativity the quadratic functional is equivalent to each of the following conditions: the nonexistence of intervals conjugate to 0, the existence of a certain conjoined basis of the associated Jacobi difference equation, the nonnegativity of certain recurrence matrices, and, under a natural additional assumption, the existence of a symmetric solution to the Riccati matrix difference equation. Moreover, an extension of the discrete Legendre condition is derived for the given discrete variational problem.

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. Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. Computers & mathematics with applications. New York: Pergamon Press, 2003, roč. 45, 6-9, s. 1369-1383. ISSN 0097-4943.

@article{488392,
   author = {Hilscher, Roman and Zeidan, Vera},
   article_location = {New York},
   article_number = {6-9},
   keywords = {discrete quadratic functional; Legendre condition; Jacobi difference equation; conjugate interval; discrete calculus of variations},
   language = {eng},
   issn = {0097-4943},
   journal = {Computers & mathematics with applications},
   title = {Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions},
   volume = {45},
   year = {2003}
}

TY  - JOUR
ID  - 488392
AU  - Hilscher, Roman - Zeidan, Vera
PY  - 2003
TI  - Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions
JF  - Computers & mathematics with applications
VL  - 45
IS  - 6-9
SP  - 1369-1383
EP  - 1369-1383
PB  - Pergamon Press
SN  - 00974943
KW  - discrete quadratic functional
KW  - Legendre condition
KW  - Jacobi difference equation
KW  - conjugate interval
KW  - discrete calculus of variations
N2  - This paper contains a complete characterization of the nonnegativity of a discrete quadratic functional with one endpoint allowed to vary. In particular, we derive the exact form and explain the role of the (strengthened) Legendre condition in the discrete calculus of variations. Under this condition, the nonnegativity the quadratic functional is equivalent to each of the following conditions: the nonexistence of intervals conjugate to 0, the existence of a certain conjoined basis of the associated Jacobi difference equation, the nonnegativity of certain recurrence matrices, and, under a natural additional assumption, the existence of a symmetric solution to the Riccati matrix difference equation. Moreover, an extension of the discrete Legendre condition is derived for the given discrete variational problem.
ER  -

HILSCHER, Roman a Vera ZEIDAN. Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions. \textit{Computers \&{} mathematics with applications}. New York: Pergamon Press, 2003, roč.~45, 6-9, s.~1369-1383. ISSN~0097-4943.

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