  An algorithm is presented for generating successive approximations to
trigonometric functions of sums of non-commuting matrices. The resulting
expressions involve nested commutators of the respective matrices. The
procedure is shown to converge in the convergent domain of the Zassenhaus
formula and can be useful in the perturbative treatment of quantum mechanical
problems, where exponentials of sums of non-commuting skew-Hermitian matrices
frequently appear.
