Hermitian Toeplitz矩阵特征值反问题

摘要

研究了通过谱数据{λ＊i}ni=1构造Hermitian Toeplitz矩阵的特征值反问题。对于Hermitian Toeplitz矩阵,根据其具有的全对称结构,可通过酉相似变换,将该问题转化为含参数的实对称矩阵特征值反问题。对于含参数的矩阵特征值反问题,用Cayley变换法求解,并给出了问题的具体算法及数值例子。%In this paper,a kind of inverse eigenvalue problem for constructing an Hermitian Toeplitz matrix from its spectral data {λ＊i}ni=1 is studied.For Hermitian Toeplitz matrix,according to its centrosymmetric structure,we transform it to the parameterized eigenvalue problems by unitary transformation.For parameterized inverse eigenvalue problems,we apply Cayley transformation method to solve this problem.Furthermore,corresponding numerical algorithms and examples are given.