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dc.contributor.authorCao, Jian
dc.contributor.authorGenton, Marc G.
dc.contributor.authorKeyes, David E.
dc.contributor.authorTurkiyyah, George M.
dc.date.accessioned2021-01-13T12:27:59Z
dc.date.available2021-01-13T12:27:59Z
dc.date.issued2021-01
dc.date.submitted2020-01-04
dc.identifier.citationCao, J., Genton, M. G., Keyes, D. E., & Turkiyyah, G. M. (2021). Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids. Computational Statistics & Data Analysis, 107165. doi:10.1016/j.csda.2020.107165
dc.identifier.issn0167-9473
dc.identifier.doi10.1016/j.csda.2020.107165
dc.identifier.urihttp://hdl.handle.net/10754/666889
dc.description.abstractThe sum of Kronecker products (SKP) representation for spatial covariance matrices from gridded observations and a corresponding adaptive-cross-approximation-based framework for building the Kronecker factors are investigated. The time cost for constructing an -dimensional covariance matrix is and the total memory footprint is , where is the number of Kronecker factors. The memory footprint under the SKP representation is compared with that under the hierarchical representation and found to be one order of magnitude smaller. A Cholesky factorization algorithm under the SKP representation is proposed and shown to factorize a one-million dimensional covariance matrix in under 600 seconds on a standard scientific workstation. With the computed Cholesky factor, simulations of Gaussian random fields in one million dimensions can be achieved at a low cost for a wide range of spatial covariance functions.
dc.description.sponsorshipThis publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST).
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S0167947320302565
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computational Statistics & Data Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computational Statistics & Data Analysis, [, , (2021-01)] DOI: 10.1016/j.csda.2020.107165 . © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleSum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentOffice of the President
dc.contributor.departmentSpatio-Temporal Statistics and Data Analysis Group
dc.contributor.departmentStatistics Program
dc.identifier.journalComputational Statistics & Data Analysis
dc.rights.embargodate2023-01-01
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Computer Science, American University of Beirut, Beirut, Lebanon.
dc.identifier.pages107165
kaust.personCao, Jian
kaust.personGenton, Marc G.
kaust.personKeyes, David E.
dc.date.accepted2020-12-24
refterms.dateFOA2021-01-13T12:29:13Z


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