Band-Times-Circulant Preconditioners for Non-Symmetric Real Toeplitz Systems with Unknown Generating Function
Year: 2022
Author: Thaniporn Chaysri, Apostolos Hadjidimos, Dimitrios Noutsos, Grigorios Tachyridis
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 285–322
Abstract
In this paper we study the preconditioning of $n×n$ non-symmetric, real Toeplitz systems, when the generating function of the coefficient matrix $T_n$ is not known a priori, but we know that a generating function $f$ exists related to the matrix sequence $\{T_n\}$, $T_n = T_n (f)$, with $f$ smooth enough. The proposed preconditioner is derived as a combination of a band Toeplitz and a circulant matrix. We give details for the construction of the proposed preconditioner, by the entries of $T_n$ and we study the cluster of the eigenvalues, as well as of the singular values, of the sequences of the coefficient matrices related to the preconditioned systems. Theoretical results prove the efficiency of the Preconditioned Generalized Minimal Residual method (PGMRES) and the Preconditioned Conjugate Gradient method of Normal Equations (PCGN). Such efficiency is also shown in demonstrating numerical examples, using the proposed preconditioning technique.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.230721.251121
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 285–322
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: Non-symmetric Toeplitz band-times-circulant preconditioner.