Further remarks on line segment curve-fitting using dynamic programming

In a recent paper, Bellman showed how dynamic programming could be used to determine the solution to a problem previously considered by Stone. The problem comprises the determination, given N, of the N points of subdivision of a given interval (&agr;, &bgr; and the corresponding line segments, that give the best least squares fit to a function g(x) in the interval. Bellman confined himself primarily to the analytical derivation, suggesting briefly, however, how the solution of the equation derived for each particular point of subdivision ui could be reduced to a discrete search. In this paper, the computational procedure is considered more fully, and the similarities to some of Stone's equations are indicated. It is further shown that an equation for u2 involving no minimization may be found. In addition, it is shown how Bellman's method may be applied to the curve-fitting problem when the additional constraints are added that the ends of the line segments must be on the curve.

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