This paper proves global convergence of the elementwise J-Jacobi method for J-Hermitian matrices under the de Rijk pivot strategy and briefly considers the asymptotic convergence of the method. Also considered is the accuracy of a new code for hyperbolic rotations of order two that employs only correctly rounded operations. The numerical tests demonstrate the advantage in the convergence speed of the J-Jacobi method under the de Rijk pivot strategy over the same method under the row-cyclic strategy for both the two-sided and the one-sided (implicit) variant of the method.
Hari et al. (Thu,) studied this question.