Detail publikace

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

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

Jazyk

en

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.

Dokumenty

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"
}