BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eike Neumann (Swansea University) DTSTART:20261015T180000Z DTEND:20261015T190000Z DTSTAMP:20261025T111746Z UID:OLS/220 DESCRIPTION:Title: Un iversal Envelopes and Applications\nby Eike Neumann (Swansea Universit y) as part of Online logic seminar\n\n\nAbstract\nComputable analysis form alizes computation with continuous objects such as real numbers and functi ons and hence offers itself as a rigorous foundation for numerical analysi s and scientific computing. It turns out\, however\, that a great many com putational problems of practical interest fail to admit computable solutio ns in the sense of computable analysis because their solutions do not depe nd continuously on the problem instance\, and computable functions must be continuous. This generally does not deter practitioners from "computing" solutions to such problems in some (typically not rigorously specified) se nse.\n\nIf we simultaneously believe that computable analysis offers the " correct" definition of computable function\, that the treatment of problem s of interest in scientific computing might require discontinuous operatio ns\, and that computable analysis can indeed serve as a rigorous foundatio n of scientific computing\, then we are led to the problem of defining wha t it might mean to "compute" discontinuous functions from the perspective of computable analysis.\n\nI will present "universal envelopes" as an atte mpt at providing such a definition. To any function f between admissible r epresented spaces\, one can assign a continuous "universal envelope"\, whi ch intuitively speaking captures the largest amount of "continuously avail able" information on f. I will discuss how universal envelopes can be used for the stability analysis of numerical programs and present some applica tions of universal envelopes to systems verification.\n LOCATION:https://researchseminars.org/talk/OLS/220/ END:VEVENT END:VCALENDAR