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The paper considers the convergence of the complex block Jacobidiagonalization methods under the large set of the generalized serial pivotstrategies. The global convergence of the block methods for Hermitian, normaland $J$-Hermitian matrices is proven. In order to obtain the convergenceresults for the block methods that solve other eigenvalue problems, such as thegeneralized eigenvalue problem, we consider the convergence of a general blockiterative process which uses the complex block Jacobi annihilators andoperators.

Convergence of the complex block Jacobi methods under the generalized serial pivot strategies