  We present improved convergence results for the Boosting Algorithm (BA), and
demonstrate that an existing formulation of the Heterogeneous Multiscale
Methods (HMM) is accurate to first order only in the macro time step,
regardless of the order of the numerical solvers employed. These results are
obtained by considering the BA and two other formulations of HMM as special
cases of a general formulation of HMM applied to dissipative stiff ordinary
differential equations.
