关于预处理与求解一类扩展的区间参数线性系统
On preconditioning and solving an extended class of interval parametric linear systems
AI总结：
针对区间参数线性系统的紧包围求解问题，本文结合右预处理、双重预处理与 p-solution 概念，扩展了可解系统类别并提升正则性检查与解集包围效率。
摘要：
我们研究区间参数线性方程组，其目标是求解此类系统，这本质上归结为寻找参数解集的一个包围。显然，我们希望该包围尽可能紧。对现有文献的回顾表明，为了使系统更易处理，大多数求解方法都使用中点逆对系统进行左预处理。令人惊讶的是，与标准区间线性系统不同，我们的研究表明，无论是在检查系统矩阵的正则性还是在包围解集方面，双重预处理都比单一预处理更有效。因此，右预处理（迄今仅在检查区间参数矩阵正则性的背景下被提及）和双重预处理，结合 p-solution 概念，使我们能够求解比大多数现有方法更广泛的一类区间参数线性系统。所提出的求解区间参数线性系统方法的适用性通过若干数值算例得到说明。
英文摘要：
We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as possible. The review of the available literature shows that in order to make a system more tractable most of the solution methods use left preconditioning of the system by the midpoint inverse. Surprisingly, and in contrast to standard interval linear systems, our investigations have shown that double preconditioning can be more efficient than a single one, both in terms of checking the regularity of the system matrix and enclosing the solution set. Consequently, right (which was hitherto mentioned in the context of checking regularity of interval parametric matrices) and double preconditioning together with the p-solution concept enable us to solve a larger class of interval parametric linear systems than most of existing methods. The applicability of the proposed approach to solving interval parametric linear systems is illustrated by several numerical examples.
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