Presented are two related numerical methods, one for the inverse eigenvalue problem for nonnegative or stochastic matrices and another for the inverse eigenvalue problem for symmetric nonnegative matrices. The methods are iterative in nature and utilize alternating projection ideas. For the symmetric problem, the main computational component of each iteration is an eigenvalue-eigenvector decomp...

In this work, the inverse eigenvalue problem is completely solved for a subfamily of clique-path graphs, in particular lollipop graphs and generalized barbell graphs. For matrix A with associated graph G, new technique utilizing strong spectral property introduced, allowing us to construct A′ whose obtained from G by appending clique while arbitrary list eigenvalues added spectrum. Consequently...