Numerical Investigation of the Spectral Distribution of Toeplitz-Function Sequences

Sean Y S HON*, Andy Wathen

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingChapterpeer-review

1 Citation (Scopus)

Abstract

Solving Toeplitz-related systems has been of interest for their ubiquitous applications, particularly in image science and the numerical treatment of differential equations. Extensive study has been carried out for Toeplitz matrices Tn∈Cn×n as well as Toeplitz-function matrices h(Tn)∈Cn×n, where h(z) is a certain function. Owing to its importance in developing effective preconditioning approaches, their spectral distribution associated with Lebesgue integrable generating functions f has been well investigated. While the spectral result concerning {h(Tn)}n is largely known, such a study is not complete when considering {Ynh(Tn)}n with Yn∈Rn×n being the anti-identity matrix. In this book chapter, we attempt to provide numerical evidence for showing that the eigenvalues of {Ynh(Tn)}n can be described by a spectral symbol which is precisely identified.

Original languageEnglish
Title of host publicationComputational Methods for Inverse Problems in Imaging
EditorsMarco Donatelli, Stefano Serra-Capizzano
PublisherSpringer, Cham
Pages77-91
Number of pages15
Edition1st
ISBN (Electronic)9783030328825
ISBN (Print)9783030328818, 9783030328849
DOIs
Publication statusPublished - 27 Nov 2019

Publication series

NameSpringer INdAM Series
Volume36
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • Asymptotic spectral distribution
  • Circulant preconditioners
  • Hankel matrices
  • Toeplitz matrices

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