qd block algorithm

The block qd algorithm is studied in order to obtain some properties about the asymptotic behavior of some eigenvalues of a block tridiagonal positive definite symmetric matrix. We prove that the eigenvalues of the first block on the block diagonal of the decomposition given by the block qd algorithm at the different stages of this algorithm constitute strictly increasing sequences and those of the last block constitute strictly decreasing sequences. Moreover the convergence of this qd algorithm is proved under certain assumptions.