{"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/adaptive-cross-approximation-with-a","title":"Adaptive Cross Approximation with a Geometrical Pivot Choice: ACA-GP Method","arxiv_id":"2502.03886","date":"2025-02-06","proceeding":null,"authors":["Vladislav A. Yastrebov","Camille Noûs"],"abstract":"The Adaptive Cross Approximation (ACA) method is widely used to approximate admissible blocks of hierarchical matrices, or H-matrices, from discretized operators in the boundary integral method. These matrices are fully populated, making their storage and manipulation resource-intensive. ACA constructs a low-rank approximation by evaluating only a few rows and columns of the original operator, significantly reducing computational costs. A key aspect of ACA's effectiveness is the selection of pivots, which are entries common to the evaluated row and column of the original matrix. This paper proposes combining the classical, purely algebraic ACA method with a geometrical pivot selection based on the central subsets and extreme property subsets. The method is named ACA-GP, GP stands for Geometrical Pivots. The superiority of the ACA-GP compared to the classical ACA is demonstrated using a classical Green operator for two clouds of interacting points.","url_abs":"https://arxiv.org/abs/2502.03886v1","url_pdf":"https://arxiv.org/pdf/2502.03886v1.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":"adaptive-cross-approximation-with-a","repo_url":"https://github.com/vyastreb/ACA","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}