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.

翻译：本文考虑了在广义串行主元策略大集合下复分块Jacobi对角化方法的收敛性。针对Hermitian矩阵、正规矩阵及$J$-Hermitian矩阵，证明了分块方法的全局收敛性。为获得求解其他特征值问题（如广义特征值问题）的分块方法的收敛性结果，我们研究了一类采用复分块Jacobi消去算子与算子的通用分块迭代过程的收敛性。