In many real-life applications, physical considerations lead to the necessity to consider the smoothest of all signals that is consistent with the measurement results. Usually, the corresponding optimization problem is solved in statistical context. In this paper, we propose a quadratic-time algorithm for smoothing anintervalfunction. This algorithm, givenn+1 intervals x0, ..., xnwith 0 ∈ x0and 0 ∈ xn, returns the vectorx0, ...,xnfor whichx0=x0=0,xi∈ xi, and Σ(xi+1−x
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