BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Sanders (Universidad Nacional Autonoma de Mexico\, Mexico) DTSTART:20210209T150000Z DTEND:20210209T160000Z DTSTAMP:20260423T024651Z UID:CRM-CAMP/30 DESCRIPTION:Title: Interval methods with Julia: Finding one million roots in one second \nby David Sanders (Universidad Nacional Autonoma de Mexico\, Mexico) as p art of CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analy sis\n\n\nAbstract\nThe Julia language provides a remarkably productive env ironment for scientific computing\, with a unique combination of interacti vity and speed\, and is particularly suitable for defining operations on n ew mathematical objects\, such as intervals.\nI will present our free / op en-source packages for interval arithmetic and interval methods (juliainte rvals.github.io)\, written in pure Julia and comparable to state-of-the-ar t libraries. They use the composability coming from Julia's "multiple-disp atch"-based design and generic programming to integrate with other package s in the "ecosystem"\, including linear algebra\, automatic differentiatio n\, and plotting.\nThe foundation is IntervalArithmetic.jl \, which is alm ost compliant with the IEEE-1788 standard. Applications currently implemen ted include root finding\, global optimization\, constraint programming\, Taylor models\, and validated integration of ODEs.\nI will also show how J ulia's facilities for parallel computing allow us to create user-defined o bjects on GPUs and manipulate them using the same Julia code. As an exampl e benchmark\, we find and verify one million stationary points of the two- dimensional transcendental Griewank function in under one second.\nJoint w ork with Luis Benet (ICF-UNAM).\n LOCATION:https://researchseminars.org/talk/CRM-CAMP/30/ END:VEVENT END:VCALENDAR