{"paper":{"title":"An exact solver for simple ${\\mathcal H}$-matrix systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jessica G\\\"ordes, Steffen B\\\"orm","submitted_at":"2014-02-21T20:15:27Z","abstract_excerpt":"Hierarchical matrices (usually abbreviated ${\\mathcal H}$-matrices) are frequently used to construct preconditioners for systems of linear equations. Since it is possible to compute approximate inverses or $LU$ factorizations in ${\\mathcal H}$-matrix representation using only ${\\mathcal O}(n \\log^2 n)$ operations, these preconditioners can be very efficient.\n  Here we consider an algorithm that allows us to solve a linear system of equations given in a simple ${\\mathcal H}$-matrix format \\emph{exactly} using ${\\mathcal O}(n \\log^2 n)$ operations. The central idea of our approach is to avoid co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5398","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"}