Volume 13, pp. 81-105, 2002.
Multigrid preconditioning and Toeplitz matrices
Thomas Huckle and Jochen Staudacher
Abstract
In this paper we discuss multigrid methods for symmetric Toeplitz
matrices. Then
the restriction and prolongation operators can be seen as projected Toeplitz
matrices. Because of the intimate connection between such matrices and
trigonometric series we can express the multigrid algorithm in terms of
the underlying functions with special zeros. This shows how to
choose the prolongation/restriction operator in order to get fast convergence.
We start by considering Toeplitz matrices with generating functions having
a single zero of finite order in
Full Text (PDF) [284 KB], BibTeX
Key words
multigrid methods, iterative methods, preconditioning, Toeplitz matrices, Fredholm integral equations, image deblurring.
AMS subject classifications
65N55, 65F10, 65F22, 65F35, 65R20.
Links to the cited ETNA articles
[3] | Vol. 6 (1997), pp. 162-181 A. Brandt and I. Livshits: Wave-ray multigrid method for standing wave equations |
ETNA articles which cite this article
Vol. 44 (2015), pp. 25-52 Matthias Bolten, Marco Donatelli, and Thomas Huckle: Analysis of smoothed aggregation multigrid methods based on Toeplitz matrices |
Vol. 53 (2020), pp. 283-312 Alessandro Buccini and Marco Donatelli: A multigrid frame based method for image deblurring |