{"paper":{"title":"A Note on QR-Based Model Reduction: Algorithm, Software, and Gravitational Wave Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.NA"],"primary_cat":"cs.DC","authors_text":"Dangxing Chen, Harbir Antil, Scott E. Field","submitted_at":"2018-05-16T04:29:33Z","abstract_excerpt":"While the proper orthogonal decomposition (POD) is optimal under certain norms it's also expensive to compute. For large matrix sizes, it is well known that the QR decomposition provides a tractable alternative. Under the assumption that it is rank--revealing QR (RRQR), the approximation error incurred is similar to the POD error and, furthermore, we show the existence of an RRQR with exactly same error estimate as POD. To numerically realize an RRQR decomposition, we will discuss the (iterative) modified Gram Schmidt with pivoting (MGS) and reduced basis method by employing a greedy strategy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06124","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}