Orthogonalization of a Direction Cosine Matrix by Iterative Techniques

It is shown that the "first inversion, transposition, and averaging" technique [1] is, assuming convergence, quadratically convergent, since it can be developed very simply by the use of quasilinearization. Only the three-dimensional case is considered; the art of matrix orthogonalization is practiced in more general settings [2] than considered here.