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A Gohberg-Semencul Type Formula for the Inverse of Conjugate-Toeplitz Matrix and Applications

A Gohberg-Semencul Type Formula for the Inverse of Conjugate-Toeplitz Matrix and Applications Constructing a kind of cyclic displacement, we obtain the inverse of conjugate-Toeplitz matrix by the aid of Gohberg-Semencul type formula. The stability of the inverse formula is discussed. Numerical examples are given to verify the feasibility of the inverse formula. We show how the analogue of our Gohberg-Semencul type formula leads to an efficient way to solve the conjugate-Toeplitz linear system of equations. It will be shown the number of real arithmetic operations is not more than known results. The corresponding conjugate-Hankel matrix is also considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A Gohberg-Semencul Type Formula for the Inverse of Conjugate-Toeplitz Matrix and Applications

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-018-0746-x
Publisher site
See Article on Publisher Site

Abstract

Constructing a kind of cyclic displacement, we obtain the inverse of conjugate-Toeplitz matrix by the aid of Gohberg-Semencul type formula. The stability of the inverse formula is discussed. Numerical examples are given to verify the feasibility of the inverse formula. We show how the analogue of our Gohberg-Semencul type formula leads to an efficient way to solve the conjugate-Toeplitz linear system of equations. It will be shown the number of real arithmetic operations is not more than known results. The corresponding conjugate-Hankel matrix is also considered.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Apr 26, 2018

References