用矩阵稀疏化完全解热带向量不等式
Complete solution of tropical vector inequalities using matrix sparsification
摘要：
我们研究的问题，找到所有解决方案的双边向量不等式在热带代数设置，未知向量乘以已知矩阵出现在两侧的不等式。我们提供了一个解决方案，使用稀疏矩阵来简化问题，并构造一个家庭的解决方案集，每个定义的稀疏矩阵从给定的矩阵之一，通过设置其某些条目为零。所有的解决方案，然后结合提出的结果在一个参数形式的矩阵，其列形成一个完整的系统的发电机的解决方案。我们描述的计算技术提出解决问题，其计算复杂性的注释，并说明这种技术与数值例子。
英文摘要：
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.
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