Publication detail

# Weakly Delayed Difference Systems in ${\mathbb R^3$ and their Solution

ŠAFAŘÍK, J. DIBLÍK, J.

Original Title

Weakly Delayed Difference Systems in ${\mathbb R^3$ and their Solution

English Title

Weakly Delayed Difference Systems in ${\mathbb R^3$ and their Solution

Type

conference paper

Language

en

Original Abstract

The paper is concerned with a weakly delayed difference system $$x(k+1) = Ax(k) + Bx(k-1)$$ where $k = 0, 1, \dots$ and $A = (a_{ij})_{i,j=1}^{3}$, $B = (b_{ij})_{i,j=1}^{3}$ are constant matrices. It is demonstrated that the initial delayed system can be transformed into a linear system without delay and, moreover, that all the eigenvalues of the matrix of the linear terms of this system can be obtained as the union of all the eigenvalues of matrices $A$ and $B$.\\ In such a case, the new linear system without delay can be solved easily, e.g., by utilizing the well-known Putzer algorithm with one of the possible cases being considered in the paper.

English abstract

The paper is concerned with a weakly delayed difference system $$x(k+1) = Ax(k) + Bx(k-1)$$ where $k = 0, 1, \dots$ and $A = (a_{ij})_{i,j=1}^{3}$, $B = (b_{ij})_{i,j=1}^{3}$ are constant matrices. It is demonstrated that the initial delayed system can be transformed into a linear system without delay and, moreover, that all the eigenvalues of the matrix of the linear terms of this system can be obtained as the union of all the eigenvalues of matrices $A$ and $B$.\\ In such a case, the new linear system without delay can be solved easily, e.g., by utilizing the well-known Putzer algorithm with one of the possible cases being considered in the paper.

Keywords

Discrete system, weak delay, initial problem, Putzer algorithm.

Released

16.06.2016

Publisher

Univerzita obrany v Brně

Location

Brno

ISBN

978-80-7231-400-3

Book

MITAV 2016 (Matematika, informační technologie a aplikované vědy), Post-conference proceedings of extended versions of selected papers

Edition number

1

Pages from

84

Pages to

104

Pages count

21

URL

Documents

BibTex

```
@inproceedings{BUT132881,
author="Jan {Šafařík} and Josef {Diblík}",
title="Weakly Delayed Difference Systems in ${\mathbb R^3$ and their Solution",
annote="The paper is concerned with a weakly delayed difference system
$$x(k+1) = Ax(k) + Bx(k-1)$$
where $k = 0, 1, \dots$ and $A = (a_{ij})_{i,j=1}^{3}$, $B = (b_{ij})_{i,j=1}^{3}$ are constant matrices.
It is demonstrated that the initial delayed system can be transformed into a linear system without delay and, moreover, that all the eigenvalues of the matrix of the linear terms of this system can be obtained as the union of all the eigenvalues of matrices $A$ and $B$.\\
In such a case, the new linear system without delay can be solved easily, e.g., by utilizing the well-known Putzer algorithm with one of the possible cases being considered in the paper.",
address="Univerzita obrany v Brně",
booktitle="MITAV 2016 (Matematika, informační technologie a aplikované vědy), Post-conference proceedings of extended versions of selected papers",
chapter="132881",
howpublished="electronic, physical medium",
institution="Univerzita obrany v Brně",
year="2016",
month="june",
pages="84--104",
publisher="Univerzita obrany v Brně",
type="conference paper"
}
```