{"paper":{"title":"Exploiting Fine Block Triangularization and Quasilinearity in Differential-Algebraic Equation Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Guangning Tan, John D. Pryce, Nedialko S. Nedialkov","submitted_at":"2014-11-15T09:14:05Z","abstract_excerpt":"The $\\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of DAE's system Jacobian is derived; this pattern implies a fine block-triangular form (BTF).\n  This article derives a simple method for quasilinearity analysis of a DAE and combines it with its fine BTF to construct a method for finding the minimal set of initial values needed for consistent initialization and a method for a block-wise computation of derivatives for the solution to the DAE."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4128","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"}