Pith Number

pith:UXEKA5QS

pith:2026:UXEKA5QSHCNVFL7XUG7LBROFMT

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Inexact versions of several block-splitting preconditioners for indefinite least squares problems

Davod Khojasteh Salkuyeh, Mohaddese Kaveh Shaldehi

Inexact block-splitting preconditioners confine all eigenvalues of the preconditioned matrix to the unit disk centered at 1 for indefinite least squares systems.

arxiv:2603.00419 v2 · 2026-02-28 · math.NA · cs.NA

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Claims

C1strongest claim

under these conditions, all eigenvalues of the preconditioned matrices are contained within a circle centered at (1,0) with radius 1. This property implies that these preconditioners are effective in accelerating the convergence of the GMRES method.

C2weakest assumption

The convergence conditions established for the stationary iterative methods hold for the special class of indefinite least squares problems considered.

C3one line summary

Inexact block-splitting preconditioners are introduced for indefinite least squares problems, with eigenvalue bounds that limit GMRES iterations and numerical tests confirming faster convergence.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, 1994 1994

[2] M. Benzi, G.H. Golub, A preconditioner for generalized saddle point problems, SIAM J. Matrix Anal. Appl. 26 (2004) 20–41 2004

[3] M. Benzi, G.H. Golub, J. Liesen, Numerical solution of saddle point problems, Acta Numer. 26 (2004) 1-137 2004

[4] A. Bojanczyk, N.J. Higham, H. Patel, Solving the indefinite least squares problem by hyperbolic QR factorization, SIAM J. Matrix Anal. Appl. 24 (2003) 914–931 2003

[5] Bojanczyk, Algorithms for indefinite linear least squares problems, Linear Algebra Appl 2021

Receipt and verification

First computed	2026-05-17T23:39:15.913217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5c8a07612389b52aff7a1beb0c5c564c503a2411957f6b0bb93480de47e7fc1

Aliases

arxiv: 2603.00419 · arxiv_version: 2603.00419v2 · doi: 10.48550/arxiv.2603.00419 · pith_short_12: UXEKA5QSHCNV · pith_short_16: UXEKA5QSHCNVFL7X · pith_short_8: UXEKA5QS

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UXEKA5QSHCNVFL7XUG7LBROFMT \
  | 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: a5c8a07612389b52aff7a1beb0c5c564c503a2411957f6b0bb93480de47e7fc1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8078f6d8ae7574e96bab687160e356080e874a4cd49324dba198487e41457ff3",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-02-28T02:37:08Z",
    "title_canon_sha256": "92c8bb642c7e7e88173aeb484592393b99d06d1eb77879a641804fdc72a572fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.00419",
    "kind": "arxiv",
    "version": 2
  }
}