广义箭状矩阵特征值及向量对反问题

Inverse Eigenvalue and Vector Pair Problem for Generalized Arrow Matrix

讨论广义箭状矩阵A两类反问题,一是特征值反问题:利用A的后顺序主子阵Aj,n的最小和最大特征值反构矩阵A;二是向量对反问题:根据给定的s维、ns+1维和n维非零实向量对(x_(u),u_(u))(x_(d),u_(d))(z,w),寻找广义箭状矩阵A,使得A1,sx_(u)=u_(u),As,nx_(d)=u_(d),Az=w.给出了此两类问题有唯一解的充分必要条件,并用数值例子验证了定理的正确性和可行性.

In the paper,two kinds of inverse problems for generalized arrow matrix A are discussed.One is to construct A from the minimum and maximum eigenvalues of its rear leading pricipal sub matrices Aj,n,that is the inverse eigenvalue problem of matrix.The other one is to find generalized arrow matrix A with given real vector pairs(x_(u),u_(u))(x_(d),u_(d))(z,w) in dimensions of s n-s+1 and n,such that A1,sx_(u)=u_(u)Asnx_(d)=u_(d) Az=w.This kind of problem is called vector pair inverse problem,Both of aboved inverse problems are given the necesarry and sufficient conditions of existing the unique solutions.Furthermore,corresponding numerical examples verify the correctness and feasibility of theorems.