The Schur Complement and the Number of Focal Points of a Symplectic Difference System

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Abstract


We present new results connecting the number of focal points of a conjoined basis of а 2n × 2n symplectic difference system and the negative inertia index of the Schur complement in a symmetric matrix of the same size. The proved result makes it possible to reduce the problem of calculating of focal points for discrete symplectic systems to a saddle point spectral problem for a symmetric indefinite block matrix.

About the authors

J V Elyseeva

Moscow State University of Technology Stankin

Email: elyseeva@gmail.com
Кафедра «Прикладная математика»; Московский государственный технологический университет «Станкин»; Moscow State University of Technology Stankin

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Copyright (c) 2011 Елисеева Ю.В.

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