{"paper":{"title":"Generalized Preconditioning and Network Flow Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jonah Sherman","submitted_at":"2016-06-23T19:56:35Z","abstract_excerpt":"We consider approximation algorithms for the problem of finding $x$ of minimal norm $\\|x\\|$ satisfying a linear system $\\mathbf{A} x = \\mathbf{b}$, where the norm $\\|\\cdot \\|$ is arbitrary and generally non-Euclidean. We show a simple general technique for composing solvers, converting iterative solvers with residual error $\\|\\mathbf{A} x - \\mathbf{b}\\| \\leq t^{-\\Omega(1)}$ into solvers with residual error $\\exp(-\\Omega(t))$, at the cost of an increase in $\\|x\\|$, by recursively invoking the solver on the residual problem $\\tilde{\\mathbf{b}} = \\mathbf{b} - \\mathbf{A} x$. Convergence of the com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07425","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"}