{"paper":{"title":"Efficient Inverse Maintenance and Faster Algorithms for Linear Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.OC"],"primary_cat":"cs.DS","authors_text":"Aaron Sidford, Yin Tat Lee","submitted_at":"2015-03-05T20:12:13Z","abstract_excerpt":"In this paper, we consider the following inverse maintenance problem: given $A \\in \\mathbb{R}^{n\\times d}$ and a number of rounds $r$, we receive a $n\\times n$ diagonal matrix $D^{(k)}$ at round $k$ and we wish to maintain an efficient linear system solver for $A^{T}D^{(k)}A$ under the assumption $D^{(k)}$ does not change too rapidly. This inverse maintenance problem is the computational bottleneck in solving multiple optimization problems. We show how to solve this problem with $\\tilde{O}(nnz(A)+d^{\\omega})$ preprocessing time and amortized $\\tilde{O}(nnz(A)+d^{2})$ time per round, improving "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01752","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":""},"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"}