{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hlibcov-parallel-hierarchical-matrix","title":"HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification","arxiv_id":"1709.08625","date":"2017-09-24","proceeding":null,"authors":["Alexander Litvinenko"],"abstract":"We provide more technical details about the HLIBCov package, which is using parallel hierarchical ($\\H$-) matrices to identify unknown parameters of the covariance function (variance, smoothness, and covariance length). These parameters are estimated by maximizing the joint Gaussian log-likelihood function. The HLIBCov package approximates large dense inhomogeneous covariance matrices with a log-linear computational cost and storage requirement. We explain how to compute the Cholesky factorization, determinant, inverse and quadratic form in the H-matrix format. To demonstrate the numerical performance, we identify three unknown parameters in an example with 2,000,000 locations on a PC-desktop.","url_abs":"http://arxiv.org/abs/1709.08625v2","url_pdf":"http://arxiv.org/pdf/1709.08625v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"hlibcov-parallel-hierarchical-matrix","repo_url":"https://github.com/litvinen/HLIBCov","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"hlibcov-parallel-hierarchical-matrix","repo_url":"https://github.com/litvinen/HLIBProCov","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}