Since for each [U.sub.k], there is a permutation matrix [P.sub.k] that makes [U.sub.k][P.sub.k] a UBCE matrix, condition A2 shows that for large enough k, each [F.sub.k][P.sub.k] will be arbitrarily close to some UBCE matrix.
The full block J-Jacobi method defined by the cyclic pivot strategy [I.sub.O], O [member of] [B.sup.(m).sub.sg], which uses UBCE J-orthogonal transformation matrices, is globally convergent.
Finally, here we show how the parameter [??] is used to avoid the assumption that the matrices [U.sub.k] from A2 have to be UBCE. Hence, for the completeness of the paper, we will present a somewhat shorter version of the proof, often referring to the proof of [18, Theorem 5.1].