Abstract
Circulant preconditioners for Hermitian Toeplitz systems are considered from the viewpoint of function theory. It is shown 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 Fejer kernels. Several circulant preconditioners are then constructed using this approach. Finally, it is proven that if the convolution product converges of f uniformly, then the circulant preconditioned Toeplitz systems will have a clustered spectrum.
| Original language | English |
|---|---|
| Pages (from-to) | 1093-1103 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 29 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Aug 1992 |
| Externally published | Yes |
Research Keywords
- Toeplitz matrix
- circulant matrix
- preconditioned conjugate gradient method
- generating function
- kernel
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