M-IHS: An accelerated randomized preconditioning method avoiding costly matrix decompositions

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buir.contributor.authorArıkan, Orhan
buir.contributor.orcidArıkan, Orhan|0000-0002-3698-8888
dc.citation.epage91en_US
dc.citation.spage57
dc.citation.volumeNumber678
dc.contributor.authorOzaslan, I. K.
dc.contributor.authorPilanci, M.
dc.contributor.authorArıkan, Orhan
dc.date.accessioned2024-03-16T12:54:34Z
dc.date.available2024-03-16T12:54:34Z
dc.date.issued2023-08-29
dc.departmentDepartment of Electrical and Electronics Engineering
dc.description.abstractMomentum Iterative Hessian Sketch ([Formula presented]) techniques, a group of solvers for large scale regularized linear Least Squares (LS) problems, are proposed and analyzed in detail. The proposed [Formula presented] techniques are obtained by incorporating Polyak's heavy ball acceleration into the Iterative Hessian Sketch algorithm and they provide significant improvements over the randomized preconditioning techniques. By solving the linear systems arising in the sub-problems during the iterations approximately, the proposed techniques are capable of avoiding all matrix decompositions and inversions, which is one of the main advantages over the alternative solvers such as the Blendenpik and the LSRN. Similar to the Chebyshev semi-iterations, the [Formula presented] variants do not use any inner products and eliminate the corresponding synchronization steps in hierarchical or distributed memory systems, yet the [Formula presented] converges faster than the Chebyshev semi-iteration based solvers. Lower bounds on the required sketch size for various randomized distributions are established through the error analyses. Unlike the previously proposed approaches to produce a solution approximation, the proposed [Formula presented] techniques can use sketch sizes that are proportional to the statistical dimension which is always smaller than the rank of the coefficient matrix. © 2023 Elsevier Inc.
dc.description.provenanceMade available in DSpace on 2024-03-16T12:54:34Z (GMT). No. of bitstreams: 1 M-IHS_An_accelerated_randomized_preconditioning_method_avoiding_costly_matrix_decompositions.pdf: 1271397 bytes, checksum: ded503464a41d7df41b19cd97f68ef15 (MD5) Previous issue date: 2023-08-29en
dc.identifier.doi10.1016/j.laa.2023.08.014
dc.identifier.urihttps://hdl.handle.net/11693/114825
dc.publisherElsevier Inc.
dc.relation.isversionofhttps://dx.doi.org/10.1016/j.laa.2023.08.014
dc.rightsCC BY 4.0 DEED (Attribution 4.0 International)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.source.titleLinear Algebra and Its Applications
dc.subjectTikhonov regularization
dc.subjectRidge regression
dc.subjectRandom projection
dc.subjectRandomized preconditioning
dc.subjectAcceleration
dc.titleM-IHS: An accelerated randomized preconditioning method avoiding costly matrix decompositions
dc.typeArticle

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