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PreprintarXiv licencearXiv

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

  • Sumit Singh
  • Shrirup Dutta
  • Sivaram Ambikasaran
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{singh2026locca,
  title = {{LoCCA: Localized Chebyshev Cross Approximation for Kernel Matrix Factorization via Nodal Perturbation Stability}},
  author = {Sumit Singh and Shrirup Dutta and Sivaram Ambikasaran},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07882},
  eprint = {2609.07882},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07882},
}
RIS
TY  - UNPB
TI  - LoCCA: Localized Chebyshev Cross Approximation for Kernel Matrix Factorization via Nodal Perturbation Stability
AU  - Sumit Singh
AU  - Shrirup Dutta
AU  - Sivaram Ambikasaran
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07882
UR  - https://arxiv.org/abs/2609.07882
AB  - 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.
ER  -