Superfast and Stable Structured Solvers for Toeplitz Least Squares via Randomized Sampling

@article{Xi2014SuperfastAS,
  title={Superfast and Stable Structured Solvers for Toeplitz Least Squares via Randomized Sampling},
  author={Yuanzhe Xi and J. Xia and Stephen Cauley and V. Balakrishnan},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2014},
  volume={35},
  pages={44-72}
}
  • Yuanzhe Xi, J. Xia, +1 author V. Balakrishnan
  • Published 2014
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • We present some superfast ($O((m+n)\log^{2}(m+n))$ complexity) and stable structured direct solvers for $m\times n$ Toeplitz least squares problems. Based on the displacement equation, a Toeplitz matrix $T$ is first transformed into a Cauchy-like matrix $\mathcal{C}$, which can be shown to have small off-diagonal numerical ranks when the diagonal blocks are rectangular. We generalize standard hierarchically semiseparable (HSS) matrix representations to rectangular ones, and construct a… CONTINUE READING
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