{"paper":{"title":"Fixed-sparsity matrix approximation from matrix-vector products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.DS","authors_text":"Cameron Musco, Christopher Musco, Diana Halikias, Feyza Duman Keles, Noah Amsel, Tyler Chen","submitted_at":"2024-02-14T18:25:13Z","abstract_excerpt":"We study the problem of approximating a matrix $\\mathbf{A}$ with a matrix that has a fixed sparsity pattern (e.g., diagonal, banded, etc.), when $\\mathbf{A}$ is accessed only by matrix-vector products. We describe a simple randomized algorithm that returns an approximation with the given sparsity pattern with Frobenius-norm error at most $(1+\\varepsilon)$ times the best possible error. When each row of the desired sparsity pattern has at most $s$ nonzero entries, this algorithm requires $O(s/\\varepsilon)$ non-adaptive matrix-vector products with $\\mathbf{A}$. We also prove a matching lower-bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.09379","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/2402.09379/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"}