THE SCHUR COMPLEMENT IN AN ALGORITHM FOR CALCULATION OF FOCAL POINTS OF CONJOINED BASES OF SYMPLECTIC DIFFERENCE SYSTEMS
Julia Elyseeva, А. А. Бондаренко · International Journal of Pure and Apllied Mathematics · 2011
We present new results connecting the number of focal points of conjoined bases of symplectic difference systems Yi+1 = WiYi, W T i JWi = J and the negative inertia index of the Schur complement (�i/Hi), where a 2n � 2n symmetric matrixi is associated with Yi and Wi. 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.