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

翻译：本文针对一类特殊有理矩阵的特征值模长界进行了推导，主要采用以下技术方法：(1) 通过将给定有理矩阵转化为关联块矩阵并应用Bauer-Fike定理，获得了特征值模长的上界；(2) 通过构造实有理函数并结合有理矩阵的Rouché定理，得到了特征值模长的下界；(3) 利用有理矩阵对应块矩阵的数值半径不等式，给出了另一种上界估计。在系数矩阵为酉矩阵的情形下，对这些界进行了比较分析。文中给出了数值算例以验证所得结果的有效性。