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DTSTART;TZID=Europe/Bucharest:20210318T100000
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DTSTAMP:20260423T080328
CREATED:20210317T151527Z
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UID:681-1616061600-1616068800@sal.cs.unibuc.ro
SUMMARY:A proof mining case study on the unit interval
DESCRIPTION:Title: A proof mining case study on the unit interval \nSpeaker: Andrei Sipoș (University of Bucharest & IMAR) \n\nAbstract:  \n\nIn 1991\, Borwein and Borwein proved [1] the following: if L>0\, f : [0\,1] → [0\,1] is L-Lipschitz\, (xn)\, (tn) ⊆ [0\,1] are such that for all n\, xn+1=(1-tn)xn+tnf(xn) and there is a δ>0 such that for all n\, tn≤(2-δ)/(L+1)\, then the sequence (xn) converges.\nThe relevant fact here is that the main argument used in their proof is of a kind that hasn’t been analyzed yet from the point of view of proof mining\, and thus it may serve as an illustrative new case study. We shall present our work [2] on the proof\, showing how to extract a uniform and computable rate of metastability for the above family of sequences.\nReferences: \n\n\n[1] D. Borwein\, J. Borwein\, Fixed point iterations for real functions. J. Math. Anal. Appl. 157\, no. 1\, 112–126\, 1991.\n[2] A. Sipoș\, Rates of metastability for iterations on the unit interval. arXiv:2008.03934 [math.CA]\, 2020.
URL:https://sal.cs.unibuc.ro/event/a-proof-mining-case-study-on-the-unit-interval/
CATEGORIES:Logic Seminar
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