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. Author manuscript; available in PMC: 2014 Nov 20.
Published in final edited form as: SIAM J Sci Comput. 2014;36(2):C95–C118. doi: 10.1137/120866580

Algorithm 2.

LSRN (computes x̂ ≈ A†b when m ≪ n).

  1. Choose an oversampling γ > 1 and set s = ⌈γm⌉.

  2. Generate G = randn(n, s), i.e., an n-by-s random matrix whose entries are independent random variables following the standard normal distribution.

  3. Compute à = AG.

  4. Compute Ã’s compact SVD ŨΣ̃ṼT, where r = rank(Ã), Ũ ∈ ℝn × r, Σ̃ ∈ ℝr × r, Ṽ ∈ ℝs × r, and only Ũ and Σ̃ are needed.

  5. Let M = ŨΣ̃−1.

  6. Compute the min-length solution to minx ‖MTAx − MTb‖2 using an iterative method, denoted by x̂.

  7. Return x̂.