BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dierk Schleicher (Aix–Marseille Université) DTSTART:20201103T140000Z DTEND:20201103T150000Z DTSTAMP:20260422T201550Z UID:CAvid/19 DESCRIPTION:Title: F inding polynomial roots using complex analysis\, dynamical systems\, compu ter algebra\nby Dierk Schleicher (Aix–Marseille Université) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstr act\nOne of the classical problems in all areas of mathematics is to find roots of complex polynomials. It is well known that this can be done only by methods of approximation. We discuss three classical methods: the Newto n\, Weierstrass\, and Ehrlich-Aberth methods\; these are complex analytic maps that\, under iteration\, are supposed to converge to one root\, resp. all roots of the polynomial. Locally\, these methods converge fast\, but the global dynamical properties are hard to describe.\n\nWe introduce thes e complex analytic dynamical systems and describe recent progress towards their global dynamical properties. In particular\, the Newton and Weierstr ass methods are not globally convergent: for open sets of polynomials ther e are open sets of initial points that fail to converge to roots. Moreover \, for Weierstrass and Ehrlich-Aberth\, there are orbits that are always d efined and converge\, but not to roots. For Newton\, there is meanwhile a rich theory about its global dynamics\, but there are many open questions for all these methods.\n\nMuch of this is joint work with members of my ER C team\, in particular my PhD student Bernhard Reinke\, as well as with co lleagues.\n LOCATION:https://researchseminars.org/talk/CAvid/19/ END:VEVENT END:VCALENDAR