{"paper":{"title":"Linear-Complexity Black-Box Randomized Compression of Rank-Structured Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"James Levitt, Per-Gunnar Martinsson","submitted_at":"2022-05-06T02:52:31Z","abstract_excerpt":"A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \\in \\mathbb{R}^{N\\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two tall thin matrices $\\Omega,\\,\\Psi \\in \\mathbb{R}^{N\\times s}$ from a suitable distribution, and then reconstructs $A$ from the information contained in the set $\\{A\\Omega,\\,\\Omega,\\,A^{*}\\Psi,\\,\\Psi\\}$. For the specific case of a \"Hierarchically Block Separable (HBS)\" matrix (a.k.a. Hierarchically Semi-Separable matrix) of block rank $k$, the number of sampl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.02990","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.02990/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}