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A Gaussian Process Regression-Enhanced Two-Sweep Parameterized Power Method for Computing Extreme Eigenpairs

  • Tiantian Sun
  • Xiaofei Peng
  • Juan Zhang
  • Seakweng Vong
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Abstract

For computing the dominant eigenvalue and the corresponding eigenvector of a real and symmetric matrix, inspired by the parameterized power method and multistep iteration, we propose a two-sweep parameterized power method, and establish its convergence theory. To further improve the convergence speed of the new method, we use Gaussian process regression (GPR) to predict the quasi-optimal parameter and give a version of the proposed method based on GPR. Numerical experiments show that the two-sweep parameterized power method with quasi-optimal parameters outperforms some existing methods in terms of computing efficiency.

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Cite

BibTeXRIS
BibTeX
@misc{sun2026gaussian,
  title = {{A Gaussian Process Regression-Enhanced Two-Sweep Parameterized Power Method for Computing Extreme Eigenpairs}},
  author = {Tiantian Sun and Xiaofei Peng and Juan Zhang and Seakweng Vong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41627},
  eprint = {2610.41627},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41627},
}
RIS
TY  - UNPB
TI  - A Gaussian Process Regression-Enhanced Two-Sweep Parameterized Power Method for Computing Extreme Eigenpairs
AU  - Tiantian Sun
AU  - Xiaofei Peng
AU  - Juan Zhang
AU  - Seakweng Vong
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41627
UR  - https://arxiv.org/abs/2610.41627
AB  - For computing the dominant eigenvalue and the corresponding eigenvector of a real and symmetric matrix, inspired by the parameterized power method and multistep iteration, we propose a two-sweep parameterized power method, and establish its convergence theory. To further improve the convergence speed of the new method, we use Gaussian process regression (GPR) to predict the quasi-optimal parameter and give a version of the proposed method based on GPR. Numerical experiments show that the two-sweep parameterized power method with quasi-optimal parameters outperforms some existing methods in terms of computing efficiency.
ER  -