由三组谱数据重构一类伪Jacobi矩阵

On the reconstruction of a pseudo-Jacobi matrix from three spectra

研究一类伪Jacobi矩阵的逆特征值问题.首先,研究此类伪Jacobi矩阵的谱性质,分两种情况讨论了此类矩阵的存在性定理,并求出相应情况下解的个数;其次,提出了一种由三组谱数据重构矩阵的算法;最后,由具体的数值实例来验证该算法的有效性.

In this paper,a class of inverse eigenvalue problems for pseudo-Jacobi matrix is studied.Firstly,we investigated the spectral properties of such pseudo-Jacobi matrices and discussed the existence of such matrices in two cases,and described the number of solutions.Then we provided an algorithm for matrix reconstruction based on three spectra.Finally,a numerical experiment was given to verify the effectiveness of the algorithm.