Preconditioners for symmetrized Toeplitz and multilevel Toeplitz matrices
Numerical Analysis
2019-04-15 v3
Abstract
When solving linear systems with nonsymmetric Toeplitz or multilevel Toeplitz matrices using Krylov subspace methods, the coefficient matrix may be symmetrized. The preconditioned MINRES method can then be applied to this symmetrized system, which allows rigorous upper bounds on the number of MINRES iterations to be obtained. However, effective preconditioners for symmetrized (multilevel) Toeplitz matrices are lacking. Here, we propose novel ideal preconditioners, and investigate the spectra of the preconditioned matrices. We show how these preconditioners can be approximated and demonstrate their effectiveness via numerical experiments.
Keywords
Cite
@article{arxiv.1812.02479,
title = {Preconditioners for symmetrized Toeplitz and multilevel Toeplitz matrices},
author = {Jennifer Pestana},
journal= {arXiv preprint arXiv:1812.02479},
year = {2019}
}
Comments
Accepted for publication in SIAM Journal on Matrix Analysis and Applications