{"paper":{"title":"Randomized QLP algorithm and error analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hua Xiang, Nianci Wu","submitted_at":"2018-11-23T01:03:24Z","abstract_excerpt":"In this paper, we describe the randomized QLP (RQLP) algorithm and its enhanced version (ERQLP) for computing the low rank approximation to $A$ of size $m\\times n$ efficiently such that $A\\approx QLP$, where $L$ is the rank-$k$ lower-triangular matrix, $Q$ and $P$ are column orthogonal matrices. The theoretical cost of the implementation of RQLP and ERQLP only needs $\\mathcal{O}(mnk)$. Moreover, we derive the upper bounds of the expected approximation error $\\mathbb{E}\\left [ (\\sigma_{j}(A) - \\sigma_{j} (L))/ \\sigma_{j}(A) \\right] $ for $j=1,\\cdots, k$, and prove that the $L$-values of the pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09334","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"}