Pith Number

pith:EV2IHI63

pith:2026:EV2IHI636I3N56TMKBJ6SI5ZRZ

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An NPDo Approach for Tensor Block-Diagonalization

Li Wang, Mei Yang, Ren-Cang Li

An NPDo method computes partial tensor block-diagonalization by maximizing the extracted block-diagonal part and converges globally while increasing the objective at each step.

arxiv:2605.12932 v1 · 2026-05-13 · math.NA · cs.NA

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Claims

C1strongest claim

It is shown the NPDo approach combined with Gauss-Seidel-type updating is globally convergent to a stationary point while the objective increases monotonically.

C2weakest assumption

The premise that maximizing the extracted block-diagonal part via mode multiplications by orthonormal matrices optimally represents the tensor for the chosen block sizes.

C3one line summary

An NPDo approach is developed for computing Principal Tensor Block-Diagonalization of tensors, generalizing Tucker decomposition and approximate tensor SVD, with a Gauss-Seidel update shown to be globally convergent to a stationary point.

References

30 extracted · 30 resolved · 1 Pith anchors

[1] Zhaojun Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vo rst (editors). Templates for the solution of Algebraic Eigenvalue Problems: A Practi cal Guide . SIAM, Philadelphia, 2000 2000

[2] G. Ballard and . G. Kolda. Tensor Decompositions for Data Science . Cambridge University Press, 2025 2025

[3] M. Bolla, G. Michaletzky, G. Tusn´ ady, and M. Ziermann. Extrema of sums of heterogeneous quadratic forms. Linear Algebra Appl. , 269(1):331–365, 1998 1998

[4] J. Chen and Y. Saad. On the tensor SVD and the optimal low rank o rthogonal approximation of tensors. SIAM J. Matrix Anal. Appl. , 30(4):1709–1734, 2009 2009

[5] De Lathauwer 2008

Receipt and verification

First computed	2026-05-18T03:09:09.908928Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

257483a3dbf236defa6c5053e923b98e728068631f1ad607342497b04ff30b9e

Aliases

arxiv: 2605.12932 · arxiv_version: 2605.12932v1 · doi: 10.48550/arxiv.2605.12932 · pith_short_12: EV2IHI636I3N · pith_short_16: EV2IHI636I3N56TM · pith_short_8: EV2IHI63

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EV2IHI636I3N56TMKBJ6SI5ZRZ \
  | 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: 257483a3dbf236defa6c5053e923b98e728068631f1ad607342497b04ff30b9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b290b1270c84ccd3c990a1c62dd12a415552baac180f29c556385626cce08fd",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T03:09:54Z",
    "title_canon_sha256": "be5389211518e81f130f6b132099d9a3188f451a4db77b7a1e9b73105d1fe9c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12932",
    "kind": "arxiv",
    "version": 1
  }
}