Robust algorithms that locate local extrema of a function of one variable from interval measurement results: A remark

The problent of h~cating local maxima and minmm of a time|ion from approximate measurement re.~ults is viud for many physical applications: in speartd mud z'i~, chemical species are klentified by IoGtting local maxima ~f the spectra; in rtuti~vatromnny, sources of celestial ~tdio emission, and their subcom|xments, are identified hy hmating hg2al nmxima of the measured brightne~ of the radio sky; ele~nenlary ]xlrtit;lea are identified hy hmating local maxima of the experimental curves. Since measurements are never absolutely precise, as a result of the measurements, we have a eJta~ ~f I.x)ssible flmctions. If we measure f ( z l ) with interval uncertainty, this class omsists tff all flmctkms f fiw which f ( ~ i ) ~ [Yi G Vl + ~], where Vl are the results tff measuring f ( z l ) , and ¢ is the measurement accuracy. For this class, ill [2], a linear-time algorithm was described. In real life, a measuring instrument can ~m|etimes malftmction, leading n) the so-Galled outliers, i.e., measurements Yi that can be way off f (a:i) (and thus do not restrict |he actual values f ( z i ) at all). In this paper, we describe robttst algorithms, i.e., algorithms that find the nttmber of kraal extrema in the presence *ff ~ s i b l e *attliers. These algorithms re,lye an imt~)rtant pra~iGll problem, but they ;|re not based on any new nmthematiGd resuhs: they simply u ~ algorithms fnm~ [9] and [3].