A finite-step construction of totally nonnegative matrices with specified eigenvalues
The authors focus on an inverse eigenvalue problem related to banded totally nonnegative (TN) matrices, which can be expressed by products of other bidiagonal TN matrices. Following an approach already presented in the literature, the authors study the eigenvalue problem from the point of view of the discrete hungry Toda (dhToda) equation. First, the determinant solution to the dhToda equation with suitable boundary conditions is presented. Then, it is shown that the characteristic polynomials of the banded TN matrices are related to the determinant solution. At last, an algorithm for constructing banded TN matrices with specified eigenvalues is given and a numerical example referring to \( 5\times 5\) TN matrices is reported.
scientific article; zbMATH DE number 6510056