{"paper":{"title":"Accuracy Directly Controlled Fast Direct Solutions of General ${\\cal H}^2$-Matrices and Its Application to Electrically Large Integral-Equation-Based Electromagnetic Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dan Jiao, Miaomiao Ma","submitted_at":"2017-03-17T18:34:30Z","abstract_excerpt":"The dense matrix resulting from an integral equation (IE) based solution of Maxwell's equations can be compactly represented by an ${\\cal H}^2$-matrix. Given a general dense ${\\cal H}^2$-matrix, prevailing fast direct solutions involve approximations whose accuracy can only be indirectly controlled. In this work, we propose new accuracy-controlled direct solution algorithms, including both factorization and inversion, for solving general ${\\cal H}^2$-matrices, which does not exist prior to this work. Different from existing direct solutions, where the cluster bases are kept unchanged in the so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06155","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"}