Sublinear-Time Quadratic Minimization via Spectral Decomposition of Matrices

@article{Levi2018SublinearTimeQM,
  title={Sublinear-Time Quadratic Minimization via Spectral Decomposition of Matrices},
  author={Amit Levi and Yuichi Yoshida},
  journal={ArXiv},
  year={2018},
  volume={abs/1806.10626}
}
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle the case where the minimization is done over a sphere. The analysis of our algorithms is obtained by combining results from graph limit theory, along with a novel spectral decomposition of matrices. Specifically, we prove that a matrix A can be decomposed into… 

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