Best one-sided approximation of polynomials under L1 norm

In this paper, we develop an analytic solution for the best one-sided approximation of polynomials under L1 norm, that is, we find two polynomials with lower degree which bound the given polynomial such that the areas between the bounding polynomials and the given polynomial attain minimum. The key ingredient of our technique is a characterization for one-sided approximations based on orthogonal polynomials. This result is applied in the degree reduction of interval polynomial/Bézier curves in Computer Aided Design.