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We consider least squares approximation of a function of one variable by acontinuous, piecewise-linear approximand that has a small number ofbreakpoints. This problem was notably considered by Bellman who proposed anapproximate algorithm based on dynamic programming. Many suboptimal approacheshave been suggested, but so far, the only exact methods resort to mixed integerprogramming with superpolynomial complexity growth.  In this paper, we present an exact and efficient algorithm based on dynamicprogramming with a hybrid value function. The achieved time-complexity seems tobe polynomial.

A Refined Algorithm for Curve Fitting by Segmented Straight Lines