An asymptotic expansion of the solution of a nonhomogeneous matrix difference equation of general form is obtained. The case when there is no bound on the differences of the arguments is considered. The effect of the roots of the characteristic equation is taken into account. The asymptotic behavior of the remainder is established depending on the asymptotics of the free term of the equation.

中文翻译：

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矩阵差分方程解的精确渐近行为

获得了一般形式的非齐次矩阵差分方程解的渐近展开。考虑在参数的差异上没有界限的情况。考虑了特征方程的根的影响。根据方程自由项的渐近性建立余数的渐近行为。