An interval union is a finite set of closed and disjoint intervals. In this paper we introduce the interval union Gauss–Seidel procedure to rigorously enclose the solution set of linear systems with uncertainties given by intervals or interval unions. We also present the interval union midpoint and Gauss–Jordan preconditioners. The Gauss–Jordan preconditioner is used in a mixed strategy to improve the quality and efficiency of the algorithm. Numerical experiments on interval linear systems generated at random show the capabilities of our approach.

中文翻译：

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使用区间联合求解具有不确定性的线性方程组

区间联合是一组有限的闭区间和不相交区间。在本文中，我们引入了区间联合 Gauss-Seidel 过程，以严格封闭具有区间或区间联合给出的不确定性的线性系统的解集。我们还介绍了区间联合中点和 Gauss-Jordan 预处理器。Gauss-Jordan 预处理器用于混合策略以提高算法的质量和效率。随机生成的区间线性系统的数值实验显示了我们方法的能力。