Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/88214
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorGuo, Xen_US
dc.creatorLin, Jen_US
dc.creatorZhou, DXen_US
dc.date.accessioned2020-09-24T02:33:40Z-
dc.date.available2020-09-24T02:33:40Z-
dc.identifier.urihttp://hdl.handle.net/10397/88214-
dc.language.isoenen_US
dc.rightsPosted with permission of the author.en_US
dc.titleConvergence of the randomized kaczmarz algorithm in Hilbert spaceen_US
dc.typePresentationen_US
dcterms.abstractThe randomized Kaczmarz algorithm recently draws much attention. Existing results on anal-ysis suffer from condition numbers of the linear equation systems. Although the randomized Kacz-marz algorithm has a natural generalization to Hilbert spaces (which covers online learning algo-rithms for a particular instance), the existing analysis does not. Although the large-scale linear equation system is an ideal scenario for the randomized Kaczmarz algorithm to outperform direct solvers, it is also a scenario the existing analysis is not satisfactory. In this research, we introduce the regularity assumption widely adopted in learning theory and obtain the polynomial convergence rate of the randomized Kaczmarz algorithm in Hilbert space under noise-free setting. We find that by nature, the randomized Kaczmarz algorithm converges weakly. Meanwhile, with noisy data, we study the relaxation method and obtain a strong convergence arbitrarily close to the minimax optimal rate. The result applies to online gradient descent learning algorithms and significantly improves the existing learning rate in literature.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationPaper presented at International Conference on Computational Harmonic Analysis 2017, Shanghai, China, 24-28 May 2017en_US
dcterms.issued2017-05-27-
dc.relation.conferenceInternational Conference on Computational Harmonic Analysisen_US
dc.description.validate202009 bcwhen_US
dc.description.oaNot applicableen_US
dc.identifier.FolderNumbera0481-n11-
dc.description.oaCategoryCopyright retained by authoren_US
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