Preconditioners for symmetrized Toeplitz and multilevel Toeplitz matrices

Pestana, J. (2019) Preconditioners for symmetrized Toeplitz and multilevel Toeplitz matrices. SIAM Journal on Matrix Analysis and Applications, 40 (3). pp. 870-887. ISSN 0895-4798 (https://doi.org/10.1137/18M1205406)

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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.

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• Item metadata

  Item type:	Article
  ID code:	67569
  Dates:	Date Event 16 July 2019 Published 10 April 2019 Accepted 3 August 2018 Submitted
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	12 Apr 2019 14:16
  Last modified:	09 Apr 2024 00:12
  Related URLs:	Journal or Publication
  URI:	https://strathprints.strath.ac.uk/id/eprint/67569