{"paper":{"title":"Factored Sparse Approximate Inverse Preconditioning via Spectral Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Francesco Brarda, Rui Peng Li, Tianshi Xu, Vassilis Kalantzis, Yuanzhe Xi","submitted_at":"2026-06-22T01:06:10Z","abstract_excerpt":"In this paper, we study value selection for fixed-pattern factorized sparse approximate inverse preconditioners. Given a prescribed sparsity pattern for a factor $G,$ we choose its admissible entries by optimizing spectral objectives of the congruent preconditioned operator $P(G)=GAG^T.$ This differs from classical sparse approximate inverse and FSAI constructions, which choose entries through algebraic Frobenius-residual criteria. For symmetric positive definite systems, the spectral target is a cluster near $+1.$ For symmetric indefinite systems, where congruence preserves inertia, we introd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22742","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22742/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}