{"paper":{"title":"Existence of $\\mathcal{H}$-matrix approximants to the inverses of BEM matrices: the simple-layer operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dirk Praetorius, Jens Markus Melenk, Markus Faustmann","submitted_at":"2013-11-20T12:08:28Z","abstract_excerpt":"We consider the question of approximating the inverse $\\mathbf W = \\mathbf V^{-1}$ of the Galerkin stiffness matrix $\\mathbf V$ obtained by discretizing the simple-layer operator $V$ with piecewise constant functions. The block partitioning of $\\mathbf W$ is assumed to satisfy any of the standard admissibility criteria that are employed in connection with clustering algorithms to approximate the discrete BEM operator $\\mathbf V$. We show that $\\mathbf W$ can be approximated by blockwise low-rank matrices such that the error decays exponentially in the block rank employed. Similar exponential a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5028","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"}