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：本文研究了在广义串行主元策略的大类下，复块Jacobi对角化方法的收敛性。证明了块方法对于Hermitian矩阵、正规矩阵及$J$-Hermitian矩阵的全局收敛性。为获得求解其他特征值问题（如广义特征值问题）的块方法的收敛结果，我们考察了使用复块Jacobi零化子与算子的广义块迭代过程的收敛性。