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Halving the size of skew-symmetric eigenvalue problems via the polar decomposition — arXiv:2608.12153

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.12153
License (as archived): CC0-1.0
Archived: 2026-10-19T05:47:35.587Z
SHA-256 of the archived text: 9730d2cdec921d84c5a3acaca7adaf8a70a87584c6e8ae5555b6de4370f61155
Stable URL of this page: https://metraipolis.com/documento/dc_6d893e6bfbc2

How to cite

Halving the size of skew-symmetric eigenvalue problems via the polar decomposition — arXiv:2608.12153 — arXiv (en), https://arxiv.org/abs/2608.12153 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_6d893e6bfbc2 (Metraipolis archive dc_6d893e6bfbc2, sha256 9730d2cdec921d84c5a3acaca7adaf8a70a87584c6e8ae5555b6de4370f61155)

BibTeX

@misc{dc6d893e6bfbc2,
  title = {Halving the size of skew-symmetric eigenvalue problems via the polar decomposition — arXiv:2608.12153},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.12153},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_6d893e6bfbc2; sha256 9730d2cdec921d84c5a3acaca7adaf8a70a87584c6e8ae5555b6de4370f61155},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.12153. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This paper introduces a novel algorithm for computing eigenvalues and eigenvectors of a dense real skew-symmetric matrix $A$. Its main ingredient is the computation of a polar factor of $A$ that is both skew-symmetric and orthogonal. This polar factor is then used to transform the original problem into a Hermitian eigenvalue problem of half the size, which can be solved accurately and efficiently with standard software such as LAPACK. Numerical experiments demonstrate the stability of the method and show that its running time is competitive with existing approaches for skew-symmetric eigenvalue problems. Finally, we show that the same principle can be used to reduce an orthogonal eigenvalue problem to a unitary eigenvalue problem of half the size.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-13 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2608.12153 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T05:40:18.097Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-13?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).