CMP.8:4.2 - Construct a family of cheaper procedures

Choose what to simplify and provide the operations that obtain the simplified answer. Possibilities include rounding values to reduce the number of states, truncating a series with a bounded tail, evaluating on a finite grid, retaining a compressed summary, or stopping an iteration once a sufficient bound is reached.

Let a parameter control the discarded information. It can be a rounding interval, polynomial degree, mesh size, retained rank, iteration count or arithmetic precision. Describe how changing it alters both the algorithm and the information retained. One parameter need not control every source of error.

If the construction changes the feasible set, provide a recovery procedure and its feasibility argument. If it changes only the objective used to select an answer, establish how that selection compares under the original objective. CMP.2 and CMP.3 can construct and schedule the resulting subproblems.

Try the simplest family that can meet the receiving requirement. A parameterized approximation scheme is unnecessary when one cheap direct calculation or an already available bound settles the question.