Peak-Reducing Fitting of a Curve under the L_p Metric

Abstract

Given a function y=f(x) in one variable, we consider the problem of computing a k-peaked curve y=φ(x) minimizing the L_p distance between them. In other words, φ(x) has at most k local peaks and minimizes the area bounded by the curves f(x) and φ(x). This gives extension of the authors’ previous work [5] on the unimodal (i.e., single-peaked) approximation for the L₂ distance.