Pith Number

pith:4UZ2QYZN

pith:2026:4UZ2QYZNDLGXY7PJVBJMNPS7FR

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Stochastic Convergence Analysis for Large-Scale Linear Discrete Ill-posed Problems

Duan-Peng Ling, Wenlong Zhang

Derives stochastic error bounds and parameter-choice rules for weighted Tikhonov regularization of large-scale ill-posed problems with random noise under a polynomial eigenvalue assumption.

arxiv:2605.18259 v1 · 2026-05-18 · math.NA · cs.NA

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\pithnumber{4UZ2QYZNDLGXY7PJVBJMNPS7FR}

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Claims

C1strongest claim

Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, stochastic error bounds are derived for weighted Tikhonov regularization under independent zero-mean bounded-variance noise (expectation bounds) and independent sub-Gaussian noise (high-probability bounds), yielding an a priori parameter-choice rule and an adaptive strategy.

C2weakest assumption

The polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator (invoked to obtain the stochastic error bounds and parameter rule).

C3one line summary

Derives stochastic error bounds and parameter-choice rules for weighted Tikhonov regularization of large-scale ill-posed problems with random noise under a polynomial eigenvalue assumption.

Receipt and verification

First computed	2026-05-20T00:05:52.480587Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e533a8632d1acd7c7de9a852c6be5f2c4fbf7650745f488238f07455f86239fc

Aliases

arxiv: 2605.18259 · arxiv_version: 2605.18259v1 · doi: 10.48550/arxiv.2605.18259 · pith_short_12: 4UZ2QYZNDLGX · pith_short_16: 4UZ2QYZNDLGXY7PJ · pith_short_8: 4UZ2QYZN

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4UZ2QYZNDLGXY7PJVBJMNPS7FR \
  | 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: e533a8632d1acd7c7de9a852c6be5f2c4fbf7650745f488238f07455f86239fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec333f723ec36f22a199b1871991ad268f112886ef6d6c9c8bf84247a9c3b7b4",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-18T11:57:22Z",
    "title_canon_sha256": "3a27da882f24c57e1bb0446c3e093acad38c7698cbdfb759c3fc879b9814b0bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18259",
    "kind": "arxiv",
    "version": 1
  }
}