论文标题
使用矩阵稀疏的完全解决热带媒介不等式的解决方案
Complete solution of tropical vector inequalities using matrix sparsification
论文作者
论文摘要
我们研究了在热带代数设置中找到的所有双面矢量不等式的解决方案的问题，在不平等的两侧，未知的矢量乘以已知矩阵的未知矢量。我们提供了一种使用稀疏矩阵来简化问题并构造解决方案集的解决方案，每个矩阵由从给定矩阵之一获得的稀疏矩阵定义，通过将其一些条目设置为零。然后将所有解决方案组合在一起，以参数形式以矩阵形式呈现结果，其列构成了解决方案的完整发电机系统。我们描述了为解决该问题而提出的计算技术，请注意其计算复杂性，并用数值示例说明了这一技术。
We examine the problem of finding all solutions of two-sided vector inequalities given in the tropical algebra setting, where the unknown vector multiplied by known matrices appears on both sides of the inequality. We offer a solution that uses sparse matrices to simplify the problem and to construct a family of solution sets, each defined by a sparse matrix obtained from one of the given matrices by setting some of its entries to zero. All solutions are then combined to present the result in a parametric form in terms of a matrix whose columns form a complete system of generators for the solution. We describe the computational technique proposed to solve the problem, remark on its computational complexity and illustrate this technique with numerical examples.
