Lower estimates on the condition number of a Toeplitz sinc matrix and related questions

Ludwig Kohaupt, Yan Wu

Research output: Contribution to journalArticlepeer-review

Abstract

As one new result, for a symmetric Toeplitz sinc n × n-matrix A(t) depending on a parameter t, lower estimates (tending to infinity as t vanishes) on the pertinent condition number are derived. A further important finding is that prior to improving the obtained lower estimates it seems to be more important to determine the lower bound on the parameter t such that the smallest eigenvalue µn(t) of A(t) can be reliably computed since this is a precondition for determining a reliable value for the condition number of the Toeplitz sinc matrix. The style of the paper is expository in order to address a large readership.

Original languageEnglish
Pages (from-to)168-182
Number of pages15
JournalConstructive Mathematical Analysis
Volume5
Issue number3
DOIs
StatePublished - 2022

Keywords

  • Condition number
  • eigenvalues and eigenvectors
  • inverse power method
  • power method
  • Toeplitz sinc matrix

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