On some inverse eigenvalue problems for Hermitian and generalized Hamiltonian/skew-Hamiltonian matrices

Some inverse eigenvalue problems for Hermitian and generalized Hamiltonian/skew-Hamiltonian matrices are discussed, including best approximation problems and eigenvalue updating problems. Based on the spectral decomposition theory on Hermitian and Hamiltonian/skew-Hamiltonian matrices, simpler parametric expressions of solutions to the general inverse eigenvalue problems are given, and then the best approximation problems and eigenvalue updating problems are solved by using these parametric expressions.