Luke, Russell

[["dc.bibliographiccitation.artnumber","13"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Fixed Point Theory and Algorithms for Sciences and Engineering"],["dc.bibliographiccitation.volume","2021"],["dc.contributor.author","Lauster, Florian"],["dc.contributor.author","Luke, Russell"],["dc.date.accessioned","2021-11-25T11:20:59Z"],["dc.date.accessioned","2022-08-18T12:23:10Z"],["dc.date.available","2021-11-25T11:20:59Z"],["dc.date.available","2022-08-18T12:23:10Z"],["dc.date.issued","2021-08-24"],["dc.date.updated","2022-07-29T12:18:24Z"],["dc.description.abstract","In the setting of CAT(κ) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessary for linearly convergent fixed point sequences, so the result is tight. To show this, we develop a theory of fixed point mappings that violate the usual assumptions of nonexpansiveness and firm nonexpansiveness in p-uniformly convex spaces."],["dc.description.sponsorship","Open-Access-Publikationsfonds 2021"],["dc.identifier.citation","Fixed Point Theory and Algorithms for Sciences and Engineering. 2021 Aug 24;2021(1):13"],["dc.identifier.doi","10.1186/s13663-021-00698-0"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/93547"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/112860"],["dc.language.iso","en"],["dc.publisher","Springer International Publishing"],["dc.relation","SFB 1456: Mathematik des Experiments: Die Herausforderung indirekter Messungen in den Naturwissenschaften"],["dc.relation","SFB 1456 | Cluster C | C02: Stochastic computed tomography: theory and algorithms for single-shot X-FEL imaging"],["dc.rights","CC BY 4.0"],["dc.rights.holder","The Author(s)"],["dc.subject","Averaged mappings"],["dc.subject","p-uniformly convex"],["dc.subject","CAT\r\n (\r\n k\r\n )\r\n \r\n $\\operatorname{CAT}(k)$\r\n space"],["dc.subject","Nonexpansive mappings"],["dc.subject","Firmly nonexpansive"],["dc.subject","Fixed point iteration"],["dc.subject","Proximal point algorithm"],["dc.title","Convergence of proximal splitting algorithms in CAT(κ) spaces and beyond"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.subtype","original_ja"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]