Matrix decompositions using sub-Gaussian random matrices

Yariv Aizenbud*, Amir Averbuch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In recent years, several algorithms which approximate matrix decomposition have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We present a new algorithm, which achieves with high probability a rank-r singular value decomposition (SVD) approximation of an n × n matrix and derive an error bound that does not depend on the first r singular values. Although the algorithm has an asymptotic complexity similar to state-of-the-art algorithms and the proven error bound is not as tight as the state-of-the-art bound, experiments show that the proposed algorithm is faster in practice while providing the same error rates as those of the stateof- the-art algorithms. We also show that an i.i.d. sub-Gaussian matrix with large probability of having null entries is metric conserving. This result is used in the SVD approximation algorithm, as well as to improve the performance of a previously proposed approximated LU decomposition algorithm.

Original languageEnglish
Pages (from-to)445-469
Number of pages25
JournalInformation and Inference
Issue number3
StatePublished - 19 Sep 2019


  • Johnson-Lindenstrauss Lemma
  • LU decomposition
  • Low-rank approximation
  • Oblivious subspace embedding
  • Random matrices
  • SVD
  • Sparse matrices
  • Sub-Gaussian matrices


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