APPROXIMATION SYSTEM

A system for generating a continuous piece-wise linear approximating function that approximately corresponds to a predetermined function over a preselected domain, the approximating function having a selected number of linear segments, the approximating function at the endpoints of the domain falling on the predetermined function. The system first selects an initial error limit, then identifies the points which define the segments. In defining the segments, the system begins at a low endpoint, extends a test segment from the low point to a high endpoint on the predetermined function, and then tests the error between the test segment and the predetermined function at each point. If the error is less than the error limit, the system selects a new higher point on the predetermined function as the new high endpoint, and repeats the operation until the test segment error between it and the predetermined function by at most the error limit. The system then extends the test segment until the error is, at most, the error limit. After determining all but the last segment, the system tests the last segment to determine whether each point is within the selected error of the approximating function. The system then adjusts the error and repeats the procedure until a termination criterion is satisfied.