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@article{701710, author = {Hilscher, Roman and Růžičková, Viera}, article_location = {Delhi (Indie)}, article_number = {1}, keywords = {Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Riccati inequality; Riccati equation; Conjoined basis; Sturmian theorem}, language = {eng}, issn = {0973-6069}, journal = {International Journal of Difference Equations}, title = {Implicit Riccati equations and quadratic functionals for discrete symplectic systems}, volume = {1}, year = {2006} }
TY - JOUR ID - 701710 AU - Hilscher, Roman - Růžičková, Viera PY - 2006 TI - Implicit Riccati equations and quadratic functionals for discrete symplectic systems JF - International Journal of Difference Equations VL - 1 IS - 1 SP - 135-154 EP - 135-154 PB - Research India Publications SN - 09736069 KW - Discrete symplectic system KW - Quadratic functional KW - Nonnegativity KW - Positivity KW - Riccati inequality KW - Riccati equation KW - Conjoined basis KW - Sturmian theorem N2 - In this paper we study discrete (implicit) Riccati matrix equations associated with discrete symplectic systems and related quadratic functionals F with variable endpoints. We derive these Riccati equations for nonnegative functionals F with separable and jointly varying endpoints. The result for jointly varying endpoints is in terms of the nonaugmented Riccati operator. The method also allows to simplify implicit Riccati equations known for the positivity of F . Finally, we establish a comparison result (Riccati inequality) for solutions of Riccati equations associated with two discrete symplectic systems. ER -
HILSCHER, Roman a Viera RŮŽIČKOVÁ. Implicit Riccati equations and quadratic functionals for discrete symplectic systems. \textit{International Journal of Difference Equations}. Delhi (Indie): Research India Publications, 2006, roč.~1, č.~1, s.~135-154. ISSN~0973-6069.
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