In this work, we investigate the interval generalized Sylvester matrix equation ${\bf{A}}X{\bf{B}}+{\bf{C}}X{\bf{D}}={\bf{F}}$ and develop some techniques for obtaining outer estimations for the so-called united solution set of this interval system. First, we propose a modified variant of the Krawczyk operator which causes reducing computational complexity to cubic, compared to Kronecker product form. We then propose an iterative technique for enclosing the solution set. These approaches are based on spectral decompositions of the midpoints of ${\bf{A}}$, ${\bf{B}}$, ${\bf{C}}$ and ${\bf{D}}$ and in both of them we suppose that the midpoints of ${\bf{A}}$ and ${\bf{C}}$ are simultaneously diagonalizable as well as for the midpoints of the matrices ${\bf{B}}$ and ${\bf{D}}$. Some numerical experiments are given to illustrate the performance of the proposed methods.

翻译：本文研究区间广义 Sylvester矩阵方程 ${\bf{A}}X{\bf{B}}+{\bf{C}}X{\bf{D}}={\bf{F}}$，并发展了若干技术以获取该区间系统所谓联合解集的外估计。首先，提出一种改进的 Krawczyk算子变体，与Kronecker积形式相比，其计算复杂度降至三次。随后，提出一种迭代技术用于包络解集。这些方法基于矩阵${\bf{A}}$、${\bf{B}}$、${\bf{C}}$和${\bf{D}}$中点谱分解，且均假设${\bf{A}}$和${\bf{C}}$的中点可同时对角化，${\bf{B}}$和${\bf{D}}$的中点亦如此。文中给出数值实验以说明所提方法的性能。