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@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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