{"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/collect-commit-expand-efficient-cpqr-based","title":"Collect, Commit, Expand: Efficient CPQR-Based Column Selection for Extremely Wide Matrices","arxiv_id":"2501.18035","date":"2025-01-29","proceeding":null,"authors":["Robin Armstrong","Anil Damle"],"abstract":"Column-pivoted QR (CPQR) factorization is a computational primitive used in numerous applications that require selecting a small set of ``representative'' columns from a much larger matrix. These include applications in spectral clustering, model-order reduction, low-rank approximation, and computational quantum chemistry, where the matrix being factorized has a moderate number of rows but an extremely large number of columns. We describe a modification of the Golub-Businger algorithm which, for many matrices of this type, can perform CPQR-based column selection much more efficiently. This algorithm, which we call CCEQR, is based on a three-step ``collect, commit, expand'' strategy that limits the number of columns being manipulated, while also transferring more computational effort from level-2 BLAS to level-3. Unlike most CPQR algorithms that exploit level-3 BLAS, CCEQR is deterministic, and provably recovers a column permutation equivalent to the one computed by the Golub-Businger algorithm. Tests on spectral clustering and Wannier basis localization problems demonstrate that on appropriately structured problems, CCEQR can significantly outperform GEQP3.","url_abs":"https://arxiv.org/abs/2501.18035v1","url_pdf":"https://arxiv.org/pdf/2501.18035v1.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":"collect-commit-expand-efficient-cpqr-based","repo_url":"https://github.com/robin-armstrong/cceqr.jl","is_official":1,"mentioned_in_paper":1,"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}