Approximate diagonalization of some Toeplitz operators and matrices

被引：0

作者：

Ahmadi Kakavandi, Bijan ^{[1
]}

Nobari, Elham ^{[2
]}

机构：

[1] Shahid Beheshti Univ, Fac Math Sci, Dept Appl Math, Tehran, Iran

[2] Univ Sci & Technol Mazandaran, Dept Math, Behshahr, Iran

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 21期

关键词：

Toeplitz operator; Toeplitz matrix; diagonalization; dimension reduction;

D O I：

10.1080/03081087.2021.1983510

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using some concepts and tools from Functional Analysis, we express explicit forms of 'eigenvectors' of two Toeplitz operators: An operator of multiplicity one, which appears e.g. in Autoregressive Process, and a banded operator of high multiplicity. Then we investigate the approximate eigenvectors of their associated Toeplitz matrices of large sizes, and after some numerical experiments, the paper concludes with an application in the principal component analysis method for dimension reduction.

引用

页码：7093 / 7114

页数：22

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