论文标题
使用矩阵稀疏来求解热带线性矢量方程
Using matrix sparsification to solve tropical linear vector equations
论文作者
论文摘要
在两个未知矢量中的线性矢量方程式在热带代数的框架中检查，该框架涉及添加的半静脉和半场的理论和应用。我们考虑一个双面方程，其中每一侧都是一个未知矢量之一给定矩阵的热带产品。我们使用矩阵稀疏技术将方程式减少到一组涉及从给定矩阵获得的行的矩阵的矢量不平等。建立了解决方案的存在条件，并以紧凑的向量形式得出解决方案的直接表示。为了说明所提出的方法并将获得的结果与现有解决方案程序的结果进行比较，我们将解决方案技术应用于文献中已知的双面方程。最后，讨论了基于得出双面方程所有解决方案的方法的计算方案。
A linear vector equation in two unknown vectors is examined in the framework of tropical algebra dealing with the theory and applications of semirings and semifields with idempotent addition. We consider a two-sided equation where each side is a tropical product of a given matrix by one of the unknown vectors. We use a matrix sparsification technique to reduce the equation to a set of vector inequalities that involve row-monomial matrices obtained from the given matrices. An existence condition of solutions for the inequalities is established, and a direct representation of the solutions is derived in a compact vector form. To illustrate the proposed approach and to compare the obtained result with that of an existing solution procedure, we apply our solution technique to handle two-sided equations known in the literature. Finally, a computational scheme based on the approach to derive all solutions of the two-sided equation is discussed.
