Circulant Preconditioners Constructed from Kernels

@inproceedings{Chan1991CirculantPC,
  title={Circulant Preconditioners Constructed from Kernels},
  author={Raymond H � Chan and Man-Chung Yeung},
  year={1991}
}
We consider circulant preconditioners for Hermitian Toeplitz systems from the view point of function theory. We show that some well-known circulant preconditioners can be derived from convoluting the generating function f of the Toeplitz matrix with famous kernels like the Dirichlet and the Fej er kernels. Several circulant precondition-ers are then constructed using this approach. Finally, we prove that if the convolution product converges to f uniformly, then the circulant preconditioned… CONTINUE READING

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Showing 1-10 of 16 references

Circulant Matrices

  • P. Davis
  • John Wiley & Sons, Inc., New York
  • 1979
Highly Influential
5 Excerpts

The Spectra of Super-optimal Circulant Preconditioned Systems

  • R. Chan, X. Jin, M. Yeung
  • SIAM J. Numer. Anal., V28
  • 1991
Highly Influential
9 Excerpts

Digital Filters

  • R. Hamming
  • 3rd Ed., Prentice Hall, New Jersey
  • 1989
Highly Influential
7 Excerpts

A Proposal for Toeplitz Matrix Calculations

  • G. Strang
  • Stud. Appl. Math., V74
  • 1986
Highly Influential
13 Excerpts

Stability of Methods for Solving Toeplitz Systems of Equations

  • J. Bunch
  • SIAM J. Sci. Statist. Comput., V6
  • 1985
Highly Influential
3 Excerpts

Approximation Theory and Numerical Linear Algebra

  • L. Trefethen
  • Al- gorithms for Approximation II, M. Cox and J…
  • 1989

The Spectrum of a Family of Circulant Precondtioned Toe-plitz Systems

  • R. Chan
  • SIAM J. Numer. Anal., V26
  • 1989
1 Excerpt

An Optimal Circulant Preconditioner for Toeplitz Systems

  • T. Chan
  • SIAM J. Sci. Statist. Comput., V9
  • 1988
1 Excerpt

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