{"paper":{"title":"Geometrical inverse preconditioning for symmetric positive definite matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jean-Paul Chehab, Marcos Raydan","submitted_at":"2015-11-24T13:20:47Z","abstract_excerpt":"We focus on inverse preconditioners based on minimizing $F(X) = 1-\\cos(XA,I)$, where $XA$ is the preconditioned matrix\n  and $A$ is symmetric and positive definite. We present and analyze gradient-type methods to minimize $F(X)$\n  on a suitable compact set. For that we use the geometrical properties of the non-polyhedral\n  cone of symmetric and positive definite matrices, and also the special properties of $F(X)$ on the feasible set.\n  Preliminary and encouraging numerical results are also presented\n  in which dense and sparse approximations are included."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07694","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"}