Linear algebraic systems involving linear dependencies between interval valued parameters and the so-called united parametric solution set of such systems are considered. The focus is on systems, such that the vertices of their interval hull solution are attained at particular endpoints of some or all parameter intervals. An essential part of finding this endpoint dependence is an initial determination of the parameters which influence the components of the solution set, and of the corresponding kind of monotonicity. In this work, we review a variety of interval approaches for the initial monotonicity proof and compare them with respect to both computational complexity and monotonicity proving efficiency. Some quantitative measures are proposed for the latter. We present a novel methodology for the initial monotonicity proof, which is highly efficient from a computational point of view, and which is also very efficient to prove the monotonicity, for a wide class of interval linear systems involving parameters with rank 1 dependency structure. The newly proposed method is illustrated on some numerical examples and compared with other approaches.

考虑了线性代数系统，该系统涉及区间值参数与此类系统的所谓联合参数解集之间的线性相关性。重点是系统，以便在某些或所有参数间隔的特定端点处获得其间隔外壳解决方案的顶点。找到此端点依赖性的重要部分是对影响解决方案集各组成部分的参数以及相应类型的单调性进行初步确定。在这项工作中，我们回顾了用于初始单调性证明的各种区间方法，并将它们在计算复杂度和单调性证明效率方面进行了比较。针对后者提出了一些定量措施。我们为初始单调性证明提供了一种新颖的方法，从计算的角度来看，它是高效的，并且对于涉及参数具有等级1依赖结构的各种区间线性系统，也非常有效地证明了单调性。在一些数值示例上说明了新提出的方法，并与其他方法进行了比较。