{"paper":{"title":"A Fast Distributed Solver for Symmetric Diagonally Dominant Linear Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Ali Jadbabaie, Haitham Bou Ammar, Rasul Tutunov","submitted_at":"2015-02-11T00:32:28Z","abstract_excerpt":"In this paper, we propose a fast distributed solver for linear equations given by symmetric diagonally dominant M-Matrices. Our approach is based on a distributed implementation of the parallel solver of Spielman and Peng by considering a specific approximated inverse chain which can be computed efficiently in a distributed fashion. Representing the system of equations by a graph $\\mathbb{G}$, the proposed distributed algorithm is capable of attaining $\\epsilon$-close solutions (for arbitrary $\\epsilon$) in time proportional to $n^{3}$ (number of nodes in $\\mathbb{G}$), ${\\alpha}$ (upper bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03158","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"}