An arbitrary band structure construction of totally nonnegative matrices with prescribed eigenvalues

An improved algorithm for solving an inverse eigenvalue problem for band matrices

“…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 authors have proposed some algorithms for constructing such band matrices with prescribed eigenvalues based on discrete integrable systems [3,4,5]. Integrable systems are nonlinear dynamical systems which have explicit solutions.…”

“…In [5], the authors introduced a discrete integrable system called the extended discrete hungry Toda equation and proposed an algorithm for constructing band oscillatory matrices with prescribed eigenvalues, of the form (1.1) with M, N general such that the prescribed data are their eigenvalues according to this equation. Any band matrix obtained from the algorithm is also a product of lower and upper bidiagonal matrices as…”

“…The aim of this paper is to improve the algorithm in the preceding paper [5]. By using the algorithm in [5], we can construct band matrices of the form (1.1) for arbitrary bandwidths M and N .…”

“…The aim of this paper is to improve the algorithm in the preceding paper [5]. By using the algorithm in [5], we can construct band matrices of the form (1.1) for arbitrary bandwidths M and N . However, there remains a large defect in the algorithm that we cannot construct generic matrices of the form (1.1) when the bandwidths M and N are not co-prime.…”