双复特征值约束下的逆二次特征值问题∗

摘要

在设计电路和带阻尼弹簧质点系统等实际问题中，求解逆特征值问题是重要的方法。本文研究了如下的电路设计问题，已知电感矩阵M、电阻矩阵C、电容矩阵K的部分信息，寻找未知量的值，使电路系统具有预先给定的频率。我们将该问题转化成了双复特征值约束下的两类逆二次特征值问题，通过求解二次特征行列式方程组，给出了问题有解的存在性条件和解的表达式。文中给出了算法和数值算例，实验结果说明了所得结论的正确性。%The inverse eigenvalue problem is an important method for designing the circuit or the mass-spring system. The paper considers the following circuit design problem: given some information of the inductance matrix M , resistance matrix C , and capacitance matrix K, determine the rest data such that the system has the prescribed frequency. We transform the problem into a quadratic inverse eigenvalue problem under double complex eigenvalues. The existence and the expression of the solution are derived by solving the quadratic character determinant equations. We present the algorithm and numerical examples, which show that the obtained result is correct.