## Abstract

We briefly describe a multigrid strategy for unilevel and two-level linear systems whose coefficient matrix A_{n} belongs either to the Toeplitz class or to the cosine algebra of type III and such that A_{n} can be naturally associated, in the spectral sense, with a polynomial function f. The interest of the technique is due to its optimal cost of O(N) arithmetic operations, where N is the size of the algebraic problem. We remark that these structures arise in certain 2D image restoration problems or can be used as preconditioners for more complicated image restoration problems.

Original language | English |
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Title of host publication | Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII |

Editors | Franklin T. LUK |

Publisher | SPIE |

Pages | 210-221 |

Number of pages | 12 |

Volume | 4791 |

DOIs | |

Publication status | Published - 6 Dec 2002 |

Externally published | Yes |

Event | International Symposium on Optical Science and Technology 2002 - Seattle, United States Duration: 7 Jul 2002 → 11 Jul 2002 |

### Symposium

Symposium | International Symposium on Optical Science and Technology 2002 |
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Country/Territory | United States |

City | Seattle |

Period | 7/07/02 → 11/07/02 |

## Keywords

- Cosine transform
- DCT-III matrix algebra
- Multigrid and preconditioning
- Toeplitz matrices
- Two-level structures