IJPAM: Volume 67, No. 4 (2011)

THE SCHUR COMPLEMENT IN AN ALGORITHM FOR
CALCULATION OF FOCAL POINTS OF CONJOINED
BASES OF SYMPLECTIC DIFFERENCE SYSTEMS

J. Elyseeva$^1$, A. Bondarenko$^2$
$^{1,2}$Department of Applied Mathematics
Moscow State University of Technology
Vadkovskii Per. 3a, Moscow, 101472, RUSSIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract. We present new results connecting the number of focal points of conjoined bases of symplectic difference systems $Y_{i+1}=W_{i}Y_{i},\,W_{i}^{T}JW_{i}=J$ and the negative inertia index of the Schur complement $(\Lambda_{i}/H_{i}),$ where a $2n\times 2n$ symmetric matrix $\Lambda_{i}$ is associated with $Y_{i}$ and $W_{i}.$ We offer an algorithm for computing eigenvalues of $2n$-order discrete Sturm Liouville eigenvalue problems based on discrete oscillation theorems and results of this paper.

Received: January 31, 2011

AMS Subject Classification: 39A10

Key Words and Phrases: Shur complement, focal points, symplectic eigenvalue problems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 4