{"paper":{"title":"Computational Complexity of Certifying Restricted Isometry Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Abhiram Natarajan, Yi Wu","submitted_at":"2014-06-23T02:08:08Z","abstract_excerpt":"Given a matrix $A$ with $n$ rows, a number $k<n$, and $0<\\delta < 1$, $A$ is $(k,\\delta)$-RIP (Restricted Isometry Property) if, for any vector $x \\in \\mathbb{R}^n$, with at most $k$ non-zero co-ordinates, $$(1-\\delta) \\|x\\|_2 \\leq \\|A x\\|_2 \\leq (1+\\delta)\\|x\\|_2$$ In many applications, such as compressed sensing and sparse recovery, it is desirable to construct RIP matrices with a large $k$ and a small $\\delta$. Given the efficacy of random constructions in generating useful RIP matrices, the problem of certifying the RIP parameters of a matrix has become important.\n  In this paper, we prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5791","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"}