We derive bounds on the absolute values 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. A numerical example is 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绝对值的界限：(1) 针对给定矩阵有理函数的关联块矩阵应用Bauer-Fike定理；(2) 关联一个实有理函数，并结合Rouché定理处理矩阵有理函数；(3) 针对矩阵有理函数的块矩阵应用数值半径不等式。当系数矩阵为酉矩阵时，对这些界限进行了比较。给出了一个数值例子以说明所得结果。