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

摘要

The problem of locating local maxima and minima of a function from approximate measurement results is vital for many physical applications: inspectral analysis, chemical species are identified by locating local maxima of the spectra; inradioastronomy, sources of celestial radio emission, and their subcomponents, are identified by locating local maxima of the measured brightness of the radio sky;elementary particlesare identified by locating local maxima of the experimental curves. Since measurements are never absolutely precise, as a result of the measurements, we have aclassof possible functions. If we measuref(xi) with interval uncertainty, this class consists of all functionsffor whichf(xi) ε yi−ɛ, yi+ɛ, whereyiare the results of measuringf(xi), andεis the measurement accuracy. For this class, in 2, a linear-time algorithm was desc