Matrix filtering as an aid to numerical integration

Digital simulation of linear systems often is complicated by the simultaneous presence of "slow" and "fast" time constants (or of small and large eigenvalues). A procedure is described that simplifies the treatment of such systems. Roughly speaking, the procedure consists of separating the response into a "low-frequency" and a "high-frequency" component, calculating each component, and then adding the results. The response separation is effected by using elementary Filter Theory ideas in a matrix context. Exact eigenvalue information is not required; a rough idea of eigenvalue locations is needed, however, to effect the responce separation.