BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tsarev S.P (Siberian Federal University\, Krasnoyarsk\, Russia) DTSTART:20200527T110000Z DTEND:20200527T120000Z DTSTAMP:20260423T022837Z UID:mmandim/1 DESCRIPTION:Title: Discrete orthogonal polynomials: anomalies of time series and boundary eff ects of polynomial filters\nby Tsarev S.P (Siberian Federal University \, Krasnoyarsk\, Russia) as part of Mathematical models and integration me thods\n\n\nAbstract\nWe describe a new result in the classical theory of u nivariate discrete orthogonal polynomials: extremely fast decay of their v alues near the interval boundary for polynomials of sufficiently high degr ee. This effect dramatically differs from the behavior of much more popula r in mathematical curricula continuous orthogonal polynomials.\n\nThe prac tical importance of this new result for the theory of discrete polynomial filters (widely applied for detection of anomalies of time series of measu rements) is demonstrated on the practical example of detection of outliers and small discontinuities in the publicly available GPS and GLONASS traje ctories.\n\nDiscrete polynomial filters\, on one hand\, can detect very sm all anomalies in sparse time series (with amplitude of order 10^(-11) rela tive to the typical values of the time series). On the other hand our gene ral result limits sensitivity of polynomial filters near the boundary of t he time series. The main problem in practical applications of the discusse d method is numerical instability of construction of the discrete orthogon al polynomials of high degree.\n\nZoom link for the talk: https://us04web. zoom.us/j/73902155099?pwd=ZnhXVUtIbUhPNmk4MFJ2dGpLNllZUT09\n LOCATION:https://researchseminars.org/talk/mmandim/1/ END:VEVENT END:VCALENDAR