Toeplitz-Circulant Preconditioners for Toeplitz Systems and their Applications to Queueing Networks with Batch Arrivals

@article{Chan1996ToeplitzCirculantPF,
  title={Toeplitz-Circulant Preconditioners for Toeplitz Systems and their Applications to Queueing Networks with Batch Arrivals},
  author={Raymond H. Chan and Wai-Ki Ching},
  journal={SIAM J. Scientific Computing},
  year={1996},
  volume={17},
  pages={762-772}
}
The preconditioned conjugate gradient method is employed to solve Toeplitz systems T n x = b where the generating functions of the n-by-n Toeplitz matrices T n are functions with zeros. In this case, circulant preconditioners are known to give poor convergence, whereas band-Toeplitz preconditioners only ooer linear convergence and can only handle real-valued functions with zeros of even orders. We here propose preconditioners which are products of band-Toeplitz matrices and circulant matrices… CONTINUE READING
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