A quadratic-time algorithm for smoothing interval functions

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 an interval function. This algorithm, given n + 1 intervals x0, . . . ,xn with 0 ∈ x0 and 0 ∈ xn, returns the vector x0, . . . , xn for which x0 = xn = 0, xi ∈ xi, and ∑ (xi+1 − xi) → min.