Randomized LU decomposition using sparse projections

Yariv Aizenbud, Gil Shabat*, Amir Averbuch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A fast algorithm that approximates a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation error of the algorithm is analyzed and a theoretical error bound is presented. Finally, numerical examples illustrate that for a similar approximation error, the sparse LU algorithm is faster than recent state-of-the-art methods. The algorithm is completely parallelizable and can fully run on a GPU. The performance is tested on a GPU card showing a significant speed-up improvement in the running time in comparison to a sequential execution.

Original languageEnglish
Pages (from-to)2525-2534
Number of pages10
JournalComputers and Mathematics with Applications
Issue number9
StatePublished - 1 Nov 2016


  • LU decomposition
  • Random matrices
  • Sparse Johnson–Lindenstrauss transform
  • Sparse matrices


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