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 Jianlin Xia and Stephen Cauley and Venkataramanan Balakrishnan},
  journal={SIAM J. Matrix Analysis Applications},
  year={2014},
  volume={35},
  pages={44-72}
}
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

Citations

Publications citing this paper.

References

Publications referenced by this paper.
SHOWING 1-10 OF 42 REFERENCES

Nested Product Decomposition of Quasiseparable Matrices

  • SIAM J. Matrix Analysis Applications
  • 2013
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

On the complexity of some hierarchical structured matrix algorithms

J. Xia
  • SIAM J. Matrix Anal. Appl., 33
  • 2012
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

New Fast Algorithms for Structured Linear Least Squares Problems

  • SIAM J. Matrix Analysis Applications
  • 1998
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Fast Solution of Toeplitz- and Cauchy-Like Least-Squares Problems

  • SIAM J. Matrix Analysis Applications
  • 2006
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL