This paper studies two inverse eigenvalue problems for two kinds of acyclic matrices whose graphs are caterpillars. The spectral data of the first problem considers the minimal and maximal eigenvalues of all leading principal submatrices of the matrix. The second consists of an extremal eigenvalue of each leading principal submatrix and one eigenpair of the matrix. In the main results, we give sufficient conditions for the existence of such matrices, and their proofs provide algorithmic procedures for their construction. Finally, we present some numerical examples that illustrate the applicability of the solutions obtained.

中文翻译：

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图为毛毛虫的两个无环矩阵的极值实现谱

本文研究了两种图为毛毛虫的无环矩阵的两个逆特征值问题。第一个问题的谱数据考虑了矩阵的所有主要主子矩阵的最小和最大特征值。第二个由每个主要主子矩阵的极值特征值和矩阵的一个特征对组成。在主要结果中，我们给出了此类矩阵存在的充分条件，并且它们的证明为它们的构造提供了算法过程。最后，我们提出了一些数值例子来说明所获得解决方案的适用性。