On approximating functions of the singular values in a stream

@article{Li2016OnAF,
  title={On approximating functions of the singular values in a stream},
  author={Yi Li and David P. Woodruff},
  journal={Proceedings of the forty-eighth annual ACM symposium on Theory of Computing},
  year={2016}
}
  • Y. Li, David P. Woodruff
  • Published 2016
  • Mathematics, Computer Science
  • Proceedings of the forty-eighth annual ACM symposium on Theory of Computing
For any real number p > 0, we nearly completely characterize the space complexity of estimating ||A||pp = ∑i=1n σip for n × n matrices A in which each row and each column has O(1) non-zero entries and whose entries are presented one at a time in a data stream model. Here the σi are the singular values of A, and when p ≥ 1, ||A||pp is the p-th power of the Schatten p-norm. We show that when p is not an even integer, to obtain a (1+є)-approximation to ||A||pp with constant probability, any 1-pass… Expand
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