Circulant Preconditioners Constructed from Kernels

  title={Circulant Preconditioners Constructed from Kernels},
  author={Raymond H � Chan and Man-Chung Yeung},
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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