{"paper":{"title":"The Matrix Chain Algorithm to Compile Linear Algebra Expressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Henrik Barthels, Paolo Bientinesi","submitted_at":"2016-11-17T12:44:15Z","abstract_excerpt":"The matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \\cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated scenarios, where expressions involve transposition, inversion, matrices with given properties, and sequences. The computation of such expressions makes use of a set of computational kernels that offer functionality well beyond the simple matrix product. The challenge then shifts from finding an optimal parenthesization to finding an optimal mapping of the inp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05660","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"}