BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ilse Ipsen (North Carolina State University\, USA) DTSTART:20200520T140000Z DTEND:20200520T150000Z DTSTAMP:20260423T040933Z UID:E-NLA/5 DESCRIPTION:Title: Pr obabilistic numerical linear solvers\nby Ilse Ipsen (North Carolina St ate University\, USA) as part of E-NLA - Online seminar series on numerica l linear algebra\n\n\nAbstract\nWe formulate iterative methods for the sol ution of nonsingular linear systems as statistical inference processes by modeling the epistemic uncertainty in the iterates due to a limited comput ational budget. The goal is to obtain well-calibrated uncertainty that is more insightful than traditional worst-case bounds\, and to produce a pr obabilistic description of the error that can be propagated coherently thr ough a computational pipeline.\n\nOur Bayesian Conjugate Gradient Method ( BayesCG) for real symmetric positive-definite linear systems posits a prio r distribution for the solution\, and conditions on the finite amount of i nformation obtained during the iterations to produce a posterior distribu tion that reflects the reduced uncertainty. The following topics will be addressed: (i) choice of prior for fast convergence and well-calibrated u ncertainty\; (ii) error estimation through test statistics that mitigate t he effect of BayesCG's nonlinear dependence on the solution\; and (iii) nu merical stability to maintain positive semi-definiteness of the posteriors \, and prevent convergence slow down from loss of orthogonality in residua ls and search directions.\n\nThis is joint work with Jon Cockayne (http:// www.joncockayne.com/)\, Chris J. Oates (http://oates.work/)\, and Timothy W. Reid (https://math.sciences.ncsu.edu/people/twreid/).\n LOCATION:https://researchseminars.org/talk/E-NLA/5/ END:VEVENT END:VCALENDAR