Computing for Eigenpairs on Globally Convergent Iterative Method for Hermitian Matrices

Let A = A* ∈ Mn and ${\cal L} = \{ (U_k, \lambda_k)|\; U_k \in {\mathbb{C}}^n, ||U_k|| = 1$ and λk∈ℝ } for k = 1,⋯,n be the set of eigenpairs of A. In this paper we develop a modified Newton method that converges to a point in $\cal L$ starting from any point in a compact subset ${\cal D} \subseteq {\mathbb{C}}^{n+1}, {\cal L} \subseteq {\cal D}\!$.