English

Note on Error Bound for Trace Approximation of Products of Toeplitz Matrices

Classical Analysis and ODEs 2022-09-07 v1 Numerical Analysis Numerical Analysis

Abstract

We investigate error orders for integral limit approximations to traces of products of Toeplitz matrices generated by integrable functions on [π,π][-\pi,\pi] having some singularities at the origin. Even though a sharp error order of the above approximation is derived in Theorem~2 of \cite{Lieberman-Phillips-2004}, its proof contains an inaccuracy as pointed out by \cite{Ginovyan-Sahakyan-2013}. In the present paper, we reinvestigate the claim given in Theorem~2 of \cite{Lieberman-Phillips-2004} and give an alternative proof of their claim.

Keywords

Cite

@article{arxiv.2209.01616,
  title  = {Note on Error Bound for Trace Approximation of Products of Toeplitz Matrices},
  author = {Tetsuya Takabatake},
  journal= {arXiv preprint arXiv:2209.01616},
  year   = {2022}
}
R2 v1 2026-06-28T00:41:55.737Z