【摘要】 <正>1 引言如下形状的n阶实对称三对角矩阵称为n阶Jacobi矩阵．振动反问题讨论由特征值(频率)和特征向量(模态)数据确定振动系统的物理参数,其研究对结构设计和结构物理参数识别具有重要意义．弹簧-质点系统的振动反问题归结为Jacobi矩阵的特征值反问题,这类问题已被许多学者研究．更多还原

【Abstract】 A kind of generalized inverse eigenvalue problem for Jacobi matrices is presented. Let A,B be Jacobi, diagonal matrices of order n, respectively,{wi}in=1 the eigenvalues of the matrix pencil {A, B}, {μi}i=1 n-1 the eigenvalues of the largest leading principle submatrix pencil of {A,B}, and u an eigenvector corresponding to the eigenvalue wi of the matrix pencil {A,B}. The problem of constructing the matrix pencil {A, B) from {wi}in=1、{μi}i=2 n-1 and u is considered. The necessary and sufficient conditions for the solvability of the problem are obtained. A numerical method for solving this problem is given.更多还原