A new Toeplitz inversion formula, stability analysis and the value

Volume 10, Issue 3, pp 1089--1097 http://dx.doi.org/10.22436/jnsa.010.03.19

Publication Date: March 20, 2017 Submission Date: June 29, 2016

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Authors

Yanpeng Zheng - Dept. of Information and Telecommunications Engineering, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea. Zunwei Fu - Dept. of Mathematics, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea. Sugoog Shon - Dept. of Information and Telecommunications Engineering, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea.

Abstract

In this paper, Toeplitz and Hankel inversion formulae are presented by the idea of skew cyclic displacement. A new Toeplitz inversion formula can be denoted as a sum of products of skew circulant matrices and upper triangular Toeplitz matrices. A new Hankel inversion formula can be denoted as a sum of products of skew left circulant matrices and upper triangular Toeplitz matrices. The stability of their inverse formulae are discussed and their algorithms are given respectively. How the analogue of our formulae lead to a more efficient way to solve the Toeplitz and Hankel linear system of equations are proposed.

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Keywords

• Toeplitz matrix
• skew circulant matrix
• inverse
• stability
• displacement transform.

MSC

•  15A09
•  15B05

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