Detail publikačního výsledku

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

ŠAFAŘÍK, J.; DIBLÍK, J.

Originální název

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

Anglický název

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

Druh

Stať ve sborníku v databázi WoS či Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

ŠAFAŘÍK, J.; DIBLÍK, J.

Rok RIV

2017

Vydáno

16.06.2016

Nakladatel

Univerzita obrany v Brně

Místo

Brno

ISBN

978-80-7231-400-3

Kniha

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

Strany od

84

Strany do

104

Strany počet

21

URL

http://mitav.unob.cz/

BibTex

@inproceedings{BUT132881,
  author="Jan {Šafařík} and Josef {Diblík}",
  title="Weakly Delayed Difference Systems in ${\mathbb R^3$ and their Solution",
  booktitle="MITAV 2016 (Matematika, informační technologie a aplikované vědy), Post-conference proceedings of extended versions of selected papers",
  year="2016",
  number="1",
  pages="84--104",
  publisher="Univerzita obrany v Brně",
  address="Brno",
  isbn="978-80-7231-400-3",
  url="http://mitav.unob.cz/"
}