Solving inverse eigenvalue problems via Householder and rank-one matrices

A brief and practical algorithm is introduced to solve symmetric inverse eigenvalue problems, which we call HROU algorithm. The algorithm is based on Householder transformations and rank one updating. We give some basic properties and the computational amount and develop sensitivity analysis of HROU algorithm. Furthermore, we develop HROU algorithm into a multi-level and adaptive one, named MLAHROU, to solve symmetric nonnegative inverse eigenvalue problems. New sufficient conditions to ensure symmetric nonnegative matrices and symmetric M-matrices are given. Many numerical examples are given to verify our theory, compare with existing results and show the efficiency of our algorithms.