Quick Approximation to Matrices and Applications

@article{Frieze1999QuickAT,
  title={Quick Approximation to Matrices and Applications},
  author={Alan M. Frieze and Ravi Kannan},
  journal={Combinatorica},
  year={1999},
  volume={19},
  pages={175-220}
}
m×n matrix A with entries between say −1 and 1, and an error parameter ε between 0 and 1, we find a matrix D (implicitly) which is the sum of simple rank 1 matrices so that the sum of entries of any submatrix (among the ) of (A−D) is at most εmn in absolute value. Our algorithm takes time dependent only on ε and the allowed probability of failure (not on m, n).We draw on two lines of research to develop the algorithms: one is built around the fundamental Regularity Lemma of Szemerédi in Graph… 

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