加边对角矩阵的逆特征值问题

Inverse Eigenvalue Problem for Bordered Diagonal Matrices

研究了由给定的2n个实数λ1>λ2>…>λn与μ1>μ2>…>μn来构造加边对角矩阵An和An*的问题,使得An以λ1,λ2,…,λn为特征值,A*n以μ1,μ2,…,μn为特征值,并且有公共对角元素α2>α3>…>αn-1,αn≠αn*.给出了这个问题有解的充要条件,并给出了相应的数值方法.

The problem on the construction of bordered diagonal matrices An and An^＊ with common diagonal elements a2〉a3〉…〉a（n-1）, a≠an^＊ in which the given 2n real numbers λ1〉λ2〉…λn and u1〉u2〉…〉un are the eigenvalues of the matrices An and An^＊, respectively. The necessary and sufficient conditions of solvability have been derived. Furthermore,numerical method has been given.