Consider a given square matrix $\textrm {K}$ with square blocks $A_{11},A_{22},\ldots,A_{nn}$ on the main diagonal. This paper aims to compute an optimal perturbation $\Delta$ of a preassigned block $A_{ii}\in\mathbb{C}^{d_i\times d_k}, \left(1\le i\le n\right)$,with respect to the spectral norm distance, such that the perturbed matrix ${\textrm {K}_X}$ has $k \le d_i$ prescribed eigenvalues. This paper presents a method for constructing the optimal perturbation by improving and extending the methodology, necessary definitions and lemmas of previous related works. Some conceivable applications of this subject are also presented. Numerical experiments are provided to illustrate the validity of the method.

翻译：考虑一个给定的方阵$\textrm {K}$，其主对角线上包含方阵块$A_{11},A_{22},\ldots,A_{nn}$。本文旨在计算预分配块$A_{ii}\in\mathbb{C}^{d_i\times d_k}, \left(1\le i\le n\right)$相对于谱范数距离的最优扰动$\Delta$，使得扰动后的矩阵${\textrm {K}_X}$具有$k \le d_i$个指定特征值。本文提出了一种构造最优扰动的方法，该方法通过改进和扩展先前相关研究的方法论、必要定义和引理来实现。同时，本文也展示了该主题一些潜在的应用场景，并通过数值实验验证了该方法的有效性。