广义Jacobi矩阵特征值反问题  

Inverse Eigenvalue Problem for Generalized Jacobi Matrices

作　　者：李志斌[1] 赵鑫鑫[1] 李伟[1] 

机构地区：[1]大连交通大学理学院,辽宁大连116028

出　　处：《大连交通大学学报》2008年第4期6-10,共5页Journal of Dalian Jiaotong University

摘　　要：提出广义Jacobi矩阵特征值反问题,也就是次对角线元素乘积为正的Jacobi矩阵的特征值反问题,问题IEPGJM:①给定两个互异实数λ,μ(λ<μ)和两个n维非零实向量x,y,求n阶实广义Jacobi矩阵J=[ai,bi,kbi],使得Jx=λx,Jy=μy;②给定3个互异实数λ,μ,γ,和3个n维非零实向量x,y,z,求n阶实广义Jacobi矩阵J=[ai,bi,ci],使得Jx=λx,Jy=μy,Jz=γz.文中给出了问题解的表达式,提供了一个数值例子.This paper presents the following inverse eigenvalue problem for generalized Jacobi matrices （a generalized Jacobi matrix has a positive product of the elements on minor diagonal）. Problem IEPGJM： ①Given real numbers λ,u（λ〈u）, and nonzero vectors x,y ∈ R^n. Find n x n real generalized Jacobi matrices J = [ ai ,bi ,kbi] to make Jx = λx ,Jy = uy. ②Given real numbers λ, u,γ（λ ≠u, λ≠ γ, u≠ γ）, and nonzero vectors x,y,z ∈ R^n . Find n × n real generalized Jacobi matrices J = [ai,bi,ci] to make Jx = λx,Jy = uy,Jz = γz. The expression of the solution of the problem is presented, and a numerical example is provided.

关 键 词：广义JACOBI矩阵 特征值 反问题 

分 类 号：O241.6[理学—计算数学]