BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christian Lubich (University of Tübingen) DTSTART:20200715T140000Z DTEND:20200715T150000Z DTSTAMP:20260423T040932Z UID:E-NLA/13 DESCRIPTION:Title: D ynamical low-rank approximation\nby Christian Lubich (University of T übingen) as part of E-NLA - Online seminar series on numerical linear alg ebra\n\n\nAbstract\nThis talk reviews differential equations and their num erical solution on manifolds of low-rank matrices or of tensors with a ran k structure such as tensor trains or general tree tensor networks. These l ow-rank differential equations serve to approximate\, in a data-compressed format\, large time-dependent matrices and tensors or multivariate functi ons that are either given explicitly via their increments or are unknown s olutions to high-dimensional evolutionary differential equations\, with mu lti-particle time-dependent Schrödinger equations and kinetic equations s uch as Vlasov equations as noteworthy examples of applications.\n\nRecentl y developed numerical time integrators are based on splitting the project ion onto the tangent space of the low-rank manifold at the current approxi mation. In contrast to all standard integrators\, these projector-splittin g methods are robust to the unavoidable presence of small singular values in the low-rank approximation. This robustness relies on exploiting geomet ric properties of the manifold of low-rank matrices or tensors: in each su bstep of the projector-splitting algorithm\, the approximation moves along a flat subspace of the low-rank manifold. In this way\, high curvature du e to small singular values does no harm.\n\nThis talk is based on work don e intermittently over the last decade with Othmar Koch\, Bart Vandereycken \, Ivan Oseledets\, Emil Kieri\, Hanna Walach and Gianluca Ceruti.\n LOCATION:https://researchseminars.org/talk/E-NLA/13/ END:VEVENT END:VCALENDAR