  The Computational Singular Perturbation (CSP) method of Lam and Goussis is an
iterative method to reduce the dimensionality of systems of ordinary
differential equations with multiple time scales. In [J. Nonlin. Sci., to
appear], the authors showed that each iteration of the CSP algorithm improves
the approximation of the slow manifold by one order. In this paper, it is shown
that the CSP method simultaneously approximates the tangent spaces to the fast
fibers along which solutions relax to the slow manifold. Again, each iteration
adds one order of accuracy. In some studies, the output of the CSP algorithm is
postprocessed by linearly projecting initial data onto the slow manifold along
these approximate tangent spaces. These projections, in turn, also become
successively more accurate.
