论文标题
关于预处理和解决扩展类别的间隔参数线性系统
On preconditioning and solving an extended class of interval parametric linear systems
论文作者
论文摘要
我们处理线性方程的间隔参数系统，目标是解决此类系统，基本上归结为寻找参数解决方案集的外壳。显然，我们希望这个围墙尽可能紧。对可用文献的审查表明，为了使系统更容易处理，大多数解决方案方法都会使用中点逆向系统进行左侧的预处理。令人惊讶的是，与标准间隔线性系统相比，我们的研究表明，在检查系统矩阵的规律性方面，双重预处理可能比单个研究更有效，并且封闭了解决方案集。因此，正确（迄今为止在检查间隔参数矩阵的规律性的上下文中提到的）和双重预处理以及P-solution概念使我们能够求解比大多数现有方法更大的间隔参数线性系统。拟议方法在求解间隔参数线性系统中的适用性由几个数值示例说明。
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.
