{"paper":{"title":"Complexity estimates for triangular hierarchical matrix algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Steffen B\\\"orm","submitted_at":"2019-05-26T16:05:48Z","abstract_excerpt":"Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\\mathcal{H}$-matrices).\n  Experiments show that using an $\\mathcal{H}$-matrix LR factorization to solve a system of linear questions is superior to direct inversion both with respect to accuracy and efficiency, but so far theoretical estimates quantifying these advantages were missing.\n  Due to a lack of symmetry in $\\mathcal{H}$-matrix algorithms, we cannot hope to prove that the LR factorization takes one third of the operations of the inversion or th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10824","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"}