Pith Number

pith:HG4C7NGJ

pith:2026:HG4C7NGJGSY52ULV4OWUIVELRY

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A refined CJ--SS--RR method with a reliable removal approach of spurious Ritz values for the Hermitian eigenvalue problem

Tianhang Liu, Zhongxiao Jia

Refined Rayleigh-Ritz projection enables tune-free removal of spurious Ritz values in Hermitian eigenproblems by exploiting unconditional convergence of refined vectors.

arxiv:2605.12846 v1 · 2026-05-13 · math.NA · cs.NA

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Claims

C1strongest claim

Exploiting the unconditional convergence of the refined Ritz vectors when the subspace is sufficiently accurate, we propose a tune-free removal approach to effectively remove spurious Ritz values with a rigorous theory supported, and develop a restarted CJ--SS--RRR algorithm. Numerical experiments show that the restarted CJ--SS--RRR algorithm is more efficient and effective than the restarted CJ--SS--RR algorithm.

C2weakest assumption

The hypothesis that the deviations of the desired eigenvectors of the matrix A from the underlying subspace tend to zero, under which the refined Ritz vectors converge unconditionally when the subspace is sufficiently accurate.

C3one line summary

Refined SS-RRR methods with a reliable tune-free removal of spurious Ritz values improve accuracy and efficiency for computing eigenpairs of large Hermitian matrices in a target region.

References

41 extracted · 41 resolved · 1 Pith anchors

[1] (eds.): Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide 2000 · doi:10.1137/1.9780898719581

[2] Davis and Yifan Hu 2011 · doi:10.1145/2049662.2049663

[3] E. Di Napoli, E. Polizzi, and Y. Saad,Efficient estimation of eigenvalue counts in an interval, Numer. Linear Algebra Appl., 23 (2016), pp. 674–692, https://doi.org/10.1002/nla.2048 2016 · doi:10.1002/nla.2048

[4] Y. Futamura and T. Sakurai,z-Pares: Parallel eigenvalue solver, 2014, https://zpares.cs. tsukuba.ac.jp/ 2014

[5] Johns Hopkins University Press, Baltimore, MD (2013) 2013 · doi:10.1137/1.9781421407944

Receipt and verification

First computed	2026-05-18T03:09:11.895877Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39b82fb4c934b1dd5175e3ad44548b8e14155463d71f1ac1f349428df781b4b1

Aliases

arxiv: 2605.12846 · arxiv_version: 2605.12846v1 · doi: 10.48550/arxiv.2605.12846 · pith_short_12: HG4C7NGJGSY5 · pith_short_16: HG4C7NGJGSY52ULV · pith_short_8: HG4C7NGJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HG4C7NGJGSY52ULV4OWUIVELRY \
  | 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: 39b82fb4c934b1dd5175e3ad44548b8e14155463d71f1ac1f349428df781b4b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4b16d97369197644b28901d426a8ae1ceab06ac6272f8ea8971e25bc339cb68",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T00:44:15Z",
    "title_canon_sha256": "2513f0a95aedd4611a7cf77b56d41e29d94377be7cee73e94d796dd10f80d3c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12846",
    "kind": "arxiv",
    "version": 1
  }
}