ABSTRACT The problem of reconstructing a matrix with a specific structure from a partial or total spectral data is known as inverse eigenvalue problem which arises in a variety of applications. In this paper, we study a partially described inverse eigenvalue problem of periodic Jacobi matrices and prove some spectral properties of such matrices. The problem involves the reconstruction of the matrix by one eigenvalue of each of its leading principal submatrices and one eigenvector of the required matrix and one more additional piece of information. The conditions for solvability of the problem are presented and finally an algorithm and some numerical results are given.

中文翻译：

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关于周期 Jacobi 矩阵的特征值反问题

摘要 从部分或全部光谱数据重建具有特定结构的矩阵的问题被称为逆特征值问题，它出现在各种应用中。在本文中，我们研究了周期性 Jacobi 矩阵的部分描述的特征值逆问题，并证明了此类矩阵的一些谱性质。该问题涉及通过其每个主要主子矩阵的一个特征值和所需矩阵的一个特征向量以及另一条附加信息来重建矩阵。给出了问题的可解性条件，最后给出了算法和一些数值结果。