箭状矩阵的一种广义特征值反问题  

Generalized inverse eigenvalue problem of arrow-like matrices

作　　者：孙玉香[1] 许勇[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《合肥工业大学学报（自然科学版）》2009年第8期1293-1296,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省教育厅自然科学基金重点资助项目(2005KJ009ZD)

摘　　要：已知系统的部分频率(特征值)和相应的振型(特征向量)即特征对,如何求质点的质量或弹簧的刚度,是振动系统中的反问题。箭状矩阵即非零元集中在主对角线、最后一行及最后一列的矩阵描述了星形弹簧质量系统的振动问题。文章对箭状矩阵提出了已知2对特征对的广义特征值反问题,并利用方程组求解的方法构造性地证明了解存在唯一的条件,同时给出了解的具体表达式及算法和实例。It is an inverse problem in the vibration system how to determine the mass of a particle or the stiffness of a spring if the partial frequency factors are known. Arrow-like matrices with all non-zeros laying in the diagonal, the last row and the last column can be used to describe the vibration problem of star-like spring-mass systems. A generalized inverse eigenvalue problem with two eigenvalues and corresponding eigenvectors of arrow-like matrices is discussed. Using the method for solving equation systems, the conditions of the existence of its unique solution and the expressions of the solution are obtained. The numerical algorithm and examples are given.

关 键 词：箭状矩阵 广义特征值 广义特征向量 反问题 

分 类 号：O151.2[理学—数学]