双特征值约束下的两类逆二次特征值问题

摘要

The paper studies two kinds of the quadratic inverse eigenvalue problem constrained by double eigenvalues, namely, solving the simultaneous equation of | λ2M+λC+K | =0, and | μ2M+μC+K =0 and getting the values of the unknown elements in the specially symmetry matrix M or K. The existence and the detailed expressions of the solutions are presented. The numerical experiments demonstrate that the algorithms are effective.%论文研究了双特征值约束下对称矩阵三元组(M、C、K)的两类逆二次特征值问题,即对于预先给定部分信息的特殊结构对称矩阵M、C、K以及两个实特征根λ和μ,通过求解|λ2M+λC+K|=0,|μ2M+μC+K|=0,联立方程组得到M或K中未知元素的值.研究给出了解的存在性和解的表达式,数值算例说明了算法的有效性.