Pith Number

pith:TNRIR4NG

pith:2026:TNRIR4NGFU7KCF6Z4UX4MMLIQL

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On a posteriori stopping rules of adaptive stochastic heavy ball method for ill-posed problems

Qinian Jin, Ruixue Gu

Adaptive stochastic heavy ball method with a posteriori stopping rule converges almost surely for ill-posed inverse problems.

arxiv:2605.13144 v1 · 2026-05-13 · math.NA · cs.NA

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3 Author claim open · sign in to claim

4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Under suitable conditions, we establish almost sure convergence as well as convergence in expectation.

C2weakest assumption

The 'suitable conditions' on the problem, noise level, adaptive parameters, and penalty functions that are required for the convergence statements to hold.

C3one line summary

An adaptive stochastic heavy ball method with a discrepancy-based a posteriori stopping rule is introduced for ill-posed inverse problems, proving almost sure and expectation convergence while improving efficiency for large systems.

References

30 extracted · 30 resolved · 0 Pith anchors

[1] R. N. Bhattacharya and E. C. W aymire. A basic course in probability theory . New York: Springer, 2007 2007

[2] R. I. Bot ¸ and T. Hein. Iterative regularization with a general penalty term-theo ry and application to L1 and TV regularization . Inverse Problems, 28 (2011), 104010 2011

[3] L. Bottou. Large-scale machine learning with stochastic gradient des cent. Proceedings of COMPSTAT2010 (Berlin: Springer), 2010, pp. 177-186 2010

[4] L. Bottou, F. E. Curtis and J. Nocedal. Optimization methods for large-scale machine learning. SIAM Review, 60 (2018), pp. 223-311 2018

[5] I. Cioranescu. Geometry of Banach spaces, duality mappings and nonlinear p roblems. Kluwer Academic Pub, 1990 1990

Receipt and verification

First computed	2026-05-18T03:08:57.353059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b6288f1a62d3ea117d9e52fc6316882d338eb1d384f398781b489a72ce6308e

Aliases

arxiv: 2605.13144 · arxiv_version: 2605.13144v1 · doi: 10.48550/arxiv.2605.13144 · pith_short_12: TNRIR4NGFU7K · pith_short_16: TNRIR4NGFU7KCF6Z · pith_short_8: TNRIR4NG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TNRIR4NGFU7KCF6Z4UX4MMLIQL \
  | 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: 9b6288f1a62d3ea117d9e52fc6316882d338eb1d384f398781b489a72ce6308e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b0c39c6491ae101048d52c0ea18a86d6f105ade235c0fd04358f19069993cb9",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T08:10:14Z",
    "title_canon_sha256": "21b488d6f4cf1e372c0c3eb1bd87ecd94453a071909426470a3b2a9851965d04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13144",
    "kind": "arxiv",
    "version": 1
  }
}