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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (1): 39-49.doi: 10.3969/j.issn.1005-3085.2015.01.005

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双复特征值约束下的逆二次特征值问题

黄贤通   

  1. 赣南师范学院数学与计算机科学学院，江西 赣州 341000
  • 收稿日期:2013-05-14 接受日期:2014-01-03 出版日期:2015-02-15 发布日期:2015-04-15
  • 基金资助:
    江西省教育厅科技项目 (GJJ10585).

Quadratic Inverse Eigenvalue Problem Under Double Complex Eigenvalues

HUANG Xian-tong   

  1. College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, Jiangxi 341000
  • Received:2013-05-14 Accepted:2014-01-03 Online:2015-02-15 Published:2015-04-15
  • Supported by:
    The Science & Research Project of Department of Education of Jiangxi Province (GJJ10585).

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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．

关键词: 二次特征值方程组, 逆二次特征值问题, 复特征值

Abstract:

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.

Key words: quadratic eigenvalue equations, quadratic inverse eigenvalue problem, complex eigenvalue

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