An improved algorithm for solving an inverse eigenvalue problem for band matrices
Kanae Akaiwa, Akira Yoshida, Koichi Kondo · Electronic Journal of Linear Algebra · 2022
The construction of matrices with prescribed eigenvalues is a kind of inverse eigenvalue problems. The authors proposed an algorithm for constructing band oscillatory matrices with prescribed eigenvalues based on the extended discrete hungry Toda equation (Numer. Algor. 75:1079--1101, 2017). In this paper, we develop a new algorithm for constructing band matrices with prescribed eigenvalues based on a generalization of the extended discrete hungry Toda equation. The new algorithm improves the previous algorithm so that the new one can produce more generic band matrices than the previous one in a certain sense. We compare the new algorithm with the previous one by numerical examples. Especially, we show an example of band oscillatory matrices which the new algorithm can produce but the previous one cannot.