{"paper":{"title":"A modified Anderson acceleration with sharp linear convergence rate predictions and application to incompressible flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Modified Anderson acceleration using nonlinear residuals gives sharp linear convergence predictions for Navier-Stokes Picard iterations.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Leo Rebholz, Yunhui He","submitted_at":"2026-05-17T21:49:19Z","abstract_excerpt":"In this work, we extend a modified Anderson acceleration proposed in [Y. He, arXiv:2603.25983, 2026] to accelerate the Picard iteration for the Navier-Stokes equations. In this variant of Anderson acceleration, named AAg, the nonlinear residual--rather than the standard fixed-point iteration residual--is used to define the associated least-squares problem. We establish a convergence analysis for this method with any depth that shows how AAg accelerates convergence through the gain of the optimization problem, and obtain a sharp prediction of its linear convergence rate (a feature that is not p"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish a convergence analysis for this method with any depth that shows how AAg accelerates convergence through the gain of the optimization problem, and obtain a sharp prediction of its linear convergence rate (a feature that is not part of the known theory for classical Anderson acceleration).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The convergence analysis assumes that the nonlinear residual is used to define the least-squares problem in AAg and that the gain of this optimization problem directly controls the contraction factor; this premise is inherited from the prior work on AAg and is not re-derived from first principles for the Navier-Stokes setting.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper introduces AAg, a nonlinear-residual variant of Anderson acceleration, proves sharp linear convergence rates for arbitrary depth on Picard iterations for Navier-Stokes, and proposes an adaptive depth strategy validated by numerical tests.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Modified Anderson acceleration using nonlinear residuals gives sharp linear convergence predictions for Navier-Stokes Picard iterations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"90f27bdfa920981467511614a1f165554de20fc89d278e9853910f7b6f8a8b76"},"source":{"id":"2605.17664","kind":"arxiv","version":1},"verdict":{"id":"00ef584e-95c2-4481-b875-e42f2cd427f0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:19:47.101946Z","strongest_claim":"We establish a convergence analysis for this method with any depth that shows how AAg accelerates convergence through the gain of the optimization problem, and obtain a sharp prediction of its linear convergence rate (a feature that is not part of the known theory for classical Anderson acceleration).","one_line_summary":"The paper introduces AAg, a nonlinear-residual variant of Anderson acceleration, proves sharp linear convergence rates for arbitrary depth on Picard iterations for Navier-Stokes, and proposes an adaptive depth strategy validated by numerical tests.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The convergence analysis assumes that the nonlinear residual is used to define the least-squares problem in AAg and that the gain of this optimization problem directly controls the contraction factor; this premise is inherited from the prior work on AAg and is not re-derived from first principles for the Navier-Stokes setting.","pith_extraction_headline":"Modified Anderson acceleration using nonlinear residuals gives sharp linear convergence predictions for Navier-Stokes Picard iterations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17664/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.467874Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:31:02.121541Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T22:21:57.393925Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T21:49:44.267700Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.538897Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:21:57.455070Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d606123ea36f483ff5c86dc9ee792f980e42d56f53e24b302e9392f7592beba9"},"references":{"count":61,"sample":[{"doi":"","year":2017,"title":"H. An, X. Jia, and H. Walker. Anderson acceleration and application to the three-temperature energy equations. Journal of Computational Physics , 347:1–19, 2017","work_id":"21f7146b-afa4-435d-b7d2-8077e2a6c929","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1965,"title":"D. G. Anderson. Iterative procedures for nonlinear integral equations. J. Assoc. Comput. Mach. , 12(4):547–560, 1965","work_id":"fe9c5d8c-6255-4e72-aeaa-b4d997bb0092","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"A. Z. Atanasov, B. Uekermann, C. Pachajoa, H. Bungartz, and P. Neumann. Steady-state Anderson accelerated coupling of Lattice Boltzmann and Navier-Stokes solvers. Comput., 4:38, 2016","work_id":"36b5c932-cacb-4096-be5a-8eec7b59d061","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"N. A. Barnafi and M. L. Pasini. 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