LSRN: A Parallel Iterative Solver for Strongly Over- or Underdetermined Systems

@article{Meng2011LSRNAP,
  title={LSRN: A Parallel Iterative Solver for Strongly Over- or Underdetermined Systems},
  author={Xiangrui Meng and Michael A. Saunders and Michael W. Mahoney},
  journal={SIAM journal on scientific computing : a publication of the Society for Industrial and Applied Mathematics},
  year={2011},
  volume={36 2},
  pages={
          C95-C118
        }
}
  • Xiangrui Meng, Michael A. Saunders, Michael W. Mahoney
  • Published in SIAM J. Scientific Computing 2011
  • Computer Science, Mathematics, Medicine
  • We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the min-length solution to min x∈ℝ n ‖Ax - b‖2, where A ∈ ℝ m × n with m ≫ n or m ≪ n, and where A may be rank-deficient. Tikhonov regularization may also be included. Since A is involved only in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and LSRN automatically speeds up when A is sparse or a fast linear operator… CONTINUE READING

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