  The paper considers the convergence of the complex block Jacobi
diagonalization methods under the large set of the generalized serial pivot
strategies. The global convergence of the block methods for Hermitian, normal
and $J$-Hermitian matrices is proven. In order to obtain the convergence
results for the block methods that solve other eigenvalue problems, such as the
generalized eigenvalue problem, we consider the convergence of a general block
iterative process which uses the complex block Jacobi annihilators and
operators.
