We derive bounds on the moduli of the eigenvalues of special type of matrix rational functions using the following techniques/methods: (1) the Bauer-Fike theorem on an associated block matrix of the given matrix rational function, (2) by associating a real rational function, along with Rouch$\text{\'e}$ theorem for the matrix rational function and (3) by a numerical radius inequality for a block matrix for the matrix rational function. These bounds are compared when the coefficients are unitary matrices. Numerical examples are given to illustrate the results obtained.

翻译：我们利用以下技巧/方法推导了特定类型矩阵有理函数特征值模的界:(1)将Bauer-Fike定理应用于给定矩阵有理函数的关联分块矩阵;(2)通过关联一个实有理函数,结合矩阵有理函数的Rouché定理;(3)通过矩阵有理函数的分块矩阵的数值半径不等式。当系数为酉矩阵时对这些界进行了比较。给出数值算例以说明所得结果。