{"paper":{"title":"Network Flows that Solve Linear Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Brian D. O. Anderson, Guodong Shi, U. Helmke","submitted_at":"2015-10-17T22:40:44Z","abstract_excerpt":"We study distributed network flows as solvers in continuous time for the linear algebraic equation $\\mathbf{z}=\\mathbf{H}\\mathbf{y}$. Each node $i$ has access to a row $\\mathbf{h}_i^{\\rm T}$ of the matrix $\\mathbf{H}$ and the corresponding entry $z_i$ in the vector $\\mathbf{z}$. The first \"consensus + projection\" flow under investigation consists of two terms, one from standard consensus dynamics and the other contributing to projection onto each affine subspace specified by the $\\mathbf{h}_i$ and $z_i$. The second \"projection consensus\" flow on the other hand simply replaces the relative stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05176","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"}