Home > ELA > Vol. 34 (2018)

#### Article Title

#### Keywords

Interval arithmetic, generalized coupled matrix equations, AE-solution set

#### Abstract

In this work, the interval generalized coupled matrix equations \begin{equation*} \sum_{j=1}^{p}{{\bf{A}}_{ij}X_{j}}+\sum_{k=1}^{q}{Y_{k}{\bf{B}}_{ik}}={\bf{C}}_{i}, \qquad i=1,\ldots,p+q, \end{equation*} are studied in which ${\bf{A}}_{ij}$, ${\bf{B}}_{ik}$ and ${\bf{C}}_{i}$ are known real interval matrices, while $X_{j}$ and $Y_{k}$ are the unknown matrices for $j=1,\ldots,p$, $k=1,\ldots,q$ and $i=1,\ldots,p+q$. This paper discusses the so-called AE-solution sets for this system. In these types of solution sets, the elements of the involved interval matrices are quantified and all occurrences of the universal quantifier $\forall$ (if any) precede the occurrences of the existential quantifier $\exists$. The AE-solution sets are characterized and some sufficient conditions under which these types of solution sets are bounded are given. Also some approaches are proposed which include a numerical technique and an algebraic approach for enclosing some types of the AE-solution sets.

#### Recommended Citation

Dehghani-Madiseh, Marzieh.
(2018),
"On the Interval Generalized Coupled Matrix Equations",
*Electronic Journal of Linear Algebra*,
Volume 34, pp. 695-717.

DOI: https://doi.org/10.13001/1081-3810, 1537-9582.3824

*Abstract*