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LoCCA: Localized Chebyshev Cross Approximation for Kernel Matrix Factorization via Nodal Perturbation Stability — arXiv:2609.07882

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.07882
License (as archived): CC0-1.0
Archived: 2026-10-16T14:48:06.228Z
SHA-256 of the archived text: 1ee177ecba4ef90a3a6f34e9d9512d646314752e7dc6e32fb01c232fff4a4a21
Stable URL of this page: https://metraipolis.com/documento/dc_b5f3bbd64cd2

How to cite

LoCCA: Localized Chebyshev Cross Approximation for Kernel Matrix Factorization via Nodal Perturbation Stability — arXiv:2609.07882 — arXiv (en), https://arxiv.org/abs/2609.07882 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_b5f3bbd64cd2 (Metraipolis archive dc_b5f3bbd64cd2, sha256 1ee177ecba4ef90a3a6f34e9d9512d646314752e7dc6e32fb01c232fff4a4a21)

BibTeX

@misc{dcb5f3bbd64cd2,
  title = {LoCCA: Localized Chebyshev Cross Approximation for Kernel Matrix Factorization via Nodal Perturbation Stability — arXiv:2609.07882},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.07882},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_b5f3bbd64cd2; sha256 1ee177ecba4ef90a3a6f34e9d9512d646314752e7dc6e32fb01c232fff4a4a21},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.07882. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We propose Local Chebyshev Cross-Approximation (LoCCA), a data-driven framework that bridges smooth polynomial interpolation with flexible matrix factorizations. LoCCA dynamically maps ideal grid nodes to their nearest physical neighbors within unstructured point sets. We support this framework with a new perturbation theory, proving that displacing Chebyshev nodes onto physical data points retains mathematical stability and accuracy without explosive error growth. Numerically, LoCCA provides strict, reliable error control even on irregular geometries where standard grid-based methods fail, achieving substantial speedups and near-optimal matrix compression.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.07882 — 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 2026-10-16T14:30:08.720Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).