Detail publikace

# Representation of solutions of higher-order linear discrete systems

Originální název

Representation of solutions of higher-order linear discrete systems

Anglický název

Representation of solutions of higher-order linear discrete systems

Jazyk

en

Originální abstrakt

A linear discrete homogenous system of the order $(m+2)$: \Delta^2 x(k) + B^2 x(k-m)= f(k), k \in\bN_0 is considered where B is a constant n \times n regular matrix, m \in \bN_0 and x\colon \{ -m, -m+1, \dots\} \to \bR^n, f\colon\bZ_0^{\infty} \rightarrow \bR^n. Two linearly independent solutions are found as a special matrix functions called delayed discrete cosine and delayed discrete sine. Utilizing these matrix functions formulas for solutions are derived. An example illustrating results is given as well.

Anglický abstrakt

A linear discrete homogenous system of the order $(m+2)$: \Delta^2 x(k) + B^2 x(k-m)= f(k), k \in\bN_0 is considered where B is a constant n \times n regular matrix, m \in \bN_0 and x\colon \{ -m, -m+1, \dots\} \to \bR^n, f\colon\bZ_0^{\infty} \rightarrow \bR^n. Two linearly independent solutions are found as a special matrix functions called delayed discrete cosine and delayed discrete sine. Utilizing these matrix functions formulas for solutions are derived. An example illustrating results is given as well.

BibTex


@inproceedings{BUT137196,
author="Josef {Diblík} and Kristýna {Mencáková}",
title="Representation of solutions of higher-order linear discrete systems",
annote="A linear discrete homogenous system of the order $(m+2)$: \Delta^2 x(k) + B^2 x(k-m)= f(k), k \in\bN_0 is considered where B is a constant n \times n regular matrix, m \in \bN_0 and x\colon \{ -m, -m+1, \dots\} \to \bR^n, f\colon\bZ_0^{\infty} \rightarrow \bR^n. Two linearly independent solutions are found as a special matrix functions called delayed discrete cosine and delayed discrete sine. Utilizing these matrix functions formulas for solutions are derived. An example illustrating results is given as well.",
}