Sharp convergence rates for averaged nonexpansive maps
Bravo
M
author
Cominetti
R
author
2018
English
We establish sharp estimates for the convergence rate of the Kranosel'skiA-Mann fixed point iteration in general normed spaces, and we use them to show that the optimal constant of asymptotic regularity is exactly . To this end we consider a nested family of optimal transport problems that provide a recursive bound for the distance between the iterates. We show that these bounds are tight by building a nonexpansive map T: [0, 1](N) -> [0, 1](N) that attains them with equality, settling a conjecture by Baillon and Bruck. The recursive bounds are in turn reinterpreted as absorption probabilities for an underlying Markov chain which is used to establish the tightness of the constant 1/root pi.
WOS:000442512900006
exported from refbase (http://ficpubs.uai.cl/show.php?record=909), last updated on Mon, 07 Jan 2019 12:33:17 +0000
text
http://ficpubs.uai.cl/files/909_Bravo+Cominetti2018.pdf
10.1007/s11856-018-1723-z
Bravo+Cominetti2018
Israel Journal Of Mathematics
Isr. J. Math.
2018
Hebrew Univ Magnes Press
continuing
periodical
academic journal
227
1
163
188
0021-2172