BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Brynjulf Owren (NTNU Trondheim) DTSTART:20240212T121500Z DTEND:20240212T130000Z DTSTAMP:20260417T004543Z UID:cam/19 DESCRIPTION:Title: Sta bility of numerical methods on Riemannian manifolds\nby Brynjulf Owren (NTNU Trondheim) as part of CAM seminar\n\nLecture held in MV:L14.\n\nAbs tract\nStability of numerical integrators play a crucial role in approxima ting the flow of differential equations. Issues related to convergence and step size limitations have been successfully resolved by studying the sta bility properties of numerical schemes. Stability also plays a role in the existence and uniqueness to the solution of the nonlinear algebraic equat ions that need to be solved in each time step for an implicit method.\nHow ever\, very little has up to now been known about stability properties of numerical methods on manifolds\, such as Lie group integrators. An interes t in these questions has recently been sparked by the efforts in construct ing ODE based neural networks that are robust against adversarial attacks. In this talk we shall discuss a new framework for B-stability on Riemanni an manifolds. A method is B-stable if the numerical method exhibits a non- expansive behaviour in the Riemannian distance measure when applied to pro blems which have non-expansive solutions.\nWe shall in particular see how the sectional curvature of the manifold plays a role\, and show some surpr ising results regarding the non-uniqueness of geodesic implicit integrator s for positively curved spaces.\n LOCATION:https://researchseminars.org/talk/cam/19/ END:VEVENT END:VCALENDAR