Investigation of the asymptotic properties of solutions to systems of discrete equations is a topic of permanent interest. Numerous papers analyze the so-called prescribed behaviour of solutions giving sufficient conditions for the existence of at least one solution having a given asymptotic behaviour. To a smaller extent the problem is considered of determining the initial data generating such solutions. The present paper finds its niche being concerned with the case of a triangular system of linear discrete equations. The existence of solutions with a prescribed asymptotic behaviour is proved and algorithms suggested for computing stepwise the initial data defining such solutions and eventually suggesting these. Illustrative examples (supported with a MATLAB program) are considered and some open problems are formulated as well.

研究离散方程组解的渐近性质是一个永久感兴趣的话题。许多论文分析了所谓的解的规定行为，为至少一个具有给定渐近行为的解的存在提供了充分条件。在较小程度上考虑确定生成此类解决方案的初始数据的问题。本论文发现它的利基是与线性离散方程的三角系统的情况有关。证明了具有指定渐近行为的解的存在性，并建议了算法来逐步计算定义此类解的初始数据并最终提出这些。考虑了说明性示例（由 MATLAB 程序支持），并且还制定了一些未解决的问题。