## Abstract

In this paper we study the use of the Sine Transform for preconditioning linear Toeplitz systems. We consider Toeplitz matrices with a real generating function that is nonnegative with only a small number of zeros. Then we can define a preconditioner of the form S_{n}ΛS_{n} where S_{n} is the matrix describing the discrete Sine transform and Λ is a diagonal matrix. If we have full knowledge about f then we can show that the preconditioned system is of bounded condition number independly of n. We can obtain the same result for the case that we know only the position and order of the zeros of f. If we only know the matrix and its coefficients t_{j}, we present Sine transform preconditioners that show in many examples the same numerical behaviour.

Original language | English |
---|---|

Pages (from-to) | 177-190 |

Number of pages | 14 |

Journal | Calcolo |

Volume | 33 |

Issue number | 3 |

DOIs | |

State | Published - 1996 |

## Keywords

- Conjugate gradient method
- Sine Transform
- Toeplitz matrix