An alternative method for continuous line segment curve-fitting

In a recent paper, the writer described an algorithm for determining the best least squares fit of N + 1 continuous line segments to a curve g(x) in an interval (α, β). The method involved the solution of functional equations in which the functional was defined over a two-dimensional space. In this paper is formulated an alternative algorithm, using a different criterion function, that reduces to consideration of a functional of one variable. The criterion function gives the best least squares fit of (constant) slopes of line segments to the derivative g′(x) of the function g(x); this leads to a class of solutions, from which is selected that which minimizes the original criterion function. An analogy to control theory along lines recently pointed out by Aoki is discussed