{"paper":{"title":"Deflation and Flexible SAP-Preconditioning of GMRES in Lattice QCD Simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-lat","authors_text":"Andrea Nobile, Andreas Frommer, Paul Zingler","submitted_at":"2012-04-24T19:25:26Z","abstract_excerpt":"The simulation of lattice QCD on massively parallel computers stimulated the development of scalable algorithms for the solution of sparse linear systems. We tackle the problem of the Wilson-Dirac operator inversion by combining a Schwarz alternating procedure (SAP) in multiplicative form with a flexible variant of the GMRES-DR algorithm. We show that restarted GMRES is not able to converge when the system is poorly conditioned. By adding deflation in the form of the FGMRES-DR algorithm, an important fraction of the information produced by the iterates is kept between successive restarts leadi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5463","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"}