{"paper":{"title":"On Sparse Reflexive Generalized Inverses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.NA"],"primary_cat":"math.OC","authors_text":"Jon Lee, Marcia Fampa","submitted_at":"2018-07-09T12:33:36Z","abstract_excerpt":"We study sparse generalized inverses $H$ of a rank-$r$ real matrix $A$. We give a construction for reflexive generalized inverses having at most $r^2$ nonzeros. For $r=1$ and for $r=2$ with $A$ nonnegative, we demonstrate how to minimize the (vector) 1-norm over reflexive generalized inverses. For general $r$, we efficiently find reflexive generalized inverses with 1-norm within approximately a factor of $r^2$ of the minimum 1-norm generalized inverse."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03074","kind":"arxiv","version":2},"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"}