A Line Segment Curve-Fitting Algorithm Related to Optimal Encoding of Information

Suppose that it is required to store as much information as possible concerning a function g(x) defined over a given interval (α, β), given that a specified amount of storage is available. This problem is closely related to that of storing N + 1 line segments joining the successive points (α, Y0), (u1, Y1), ···, (uN, YN), (β, YN+1), given N, the uj and Yj being determined such that the lines give the best least squares fit to the curve. A computational algorithm is determined for solving this problem in general, and it is shown how the points are determined when the uj and Yj are constrained, for example, to integer values. The method used is similar to that used in recent line-segment curve-fitting papers by Bellman and by Gluss. Finally, the information encoding aspects of the model are discussed.