Pith Number

pith:4JLKUCGV

pith:2026:4JLKUCGVTLFOMJIIJUN2T2EN2K

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A modified Anderson acceleration with sharp linear convergence rate predictions and application to incompressible flows

Leo Rebholz, Yunhui He

Modified Anderson acceleration using nonlinear residuals gives sharp linear convergence predictions for Navier-Stokes Picard iterations.

arxiv:2605.17664 v1 · 2026-05-17 · math.NA · cs.NA

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Claims

C1strongest 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).

C2weakest 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.

C3one 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.

References

61 extracted · 61 resolved · 0 Pith anchors

[1] 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 2017

[2] D. G. Anderson. Iterative procedures for nonlinear integral equations. J. Assoc. Comput. Mach. , 12(4):547–560, 1965 1965

[3] 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 2016

[4] N. A. Barnafi and M. L. Pasini. Two-level sketching alternating Anderson acceleration for complex physics applications. arXiv preprint arXiv:2505.08587 , 2025 2025

[5] M. Benzi and M. Olshanskii. An augmented Lagrangian-based approach to the Oseen problem. SIAM J. Sci. Comput. , 28:2095–2113, 2006 2095

Receipt and verification

First computed	2026-05-20T00:04:51.591997Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e256aa08d59acae625084d1ba9e88dd295157d0575795ddb9bfc5821beed4616

Aliases

arxiv: 2605.17664 · arxiv_version: 2605.17664v1 · doi: 10.48550/arxiv.2605.17664 · pith_short_12: 4JLKUCGVTLFO · pith_short_16: 4JLKUCGVTLFOMJII · pith_short_8: 4JLKUCGV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4JLKUCGVTLFOMJIIJUN2T2EN2K \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e256aa08d59acae625084d1ba9e88dd295157d0575795ddb9bfc5821beed4616

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53e5ff034f433036672d6ef546db80b4adfb35b7dbdb398d65dec40503f93919",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-17T21:49:19Z",
    "title_canon_sha256": "7dffdd3152a98e5faee26ecc7fb3b1485eb76480f44a982fc0966481e074b250"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17664",
    "kind": "arxiv",
    "version": 1
  }
}