  We obtain local (i.e., linearized) convergence conditions for iterative
methods that seek solitary waves with prescribed values of quadratic conserved
quantities of multi-component Hamiltonian nonlinear wave equations. These
conditions extend the ones found for single-component solitary waves in [J.
Yang and T.I. Lakoba, Stud. Appl. Math. {\bf 120}, 265--292 (2008)]. We also
show that, and why, these convergence conditions coincide with dynamical
stability conditions for ground-state solitary waves.
