Selected Papers from The China-Korea-USA International Conference on Matrix Theory with Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 4671

Special Issue Editors


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Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, China
Interests: linear and multilinear algebra; numerical linear algebra; matrix theory with application

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Guest Editor
Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302, USA
Interests: combinatorial matrix theory; sign pattern matrices; oriented matroids; convex polytopes; algebraic graph theory

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Guest Editor
Department of Mathematics, University of Manitoba, Winnipeg, MB R2M 0T8, Canada
Interests: algebra; computer algebra; applications of computer algebra
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Special Issue Information

Dear Colleagues,

The China–Korea–USA International Conference on Matrix Theory with Applications (IRCTMT-AORC Joint Meeting) took place in Hainan, China, on 25–28 November 2021.

The purpose of the conference is to stimulate research and foster the interaction of researchers interested in matrix theory and its applications. The conference hopes to provide a convenient platform for the exchange of research experiences and ideas from different research areas related to matrix theory and its applications.

Topics covered include (but are not limited to) all the research areas of matrix theory and its applications.

Prof. Dr. Qing-Wen Wang
Prof. Dr. Zhongshan Li
Prof. Dr. Yang Zhang
Guest Editors

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Keywords

  • matrix theory
  • numerical linear algebra
  • matrix decompositions
  • eigenvalue of matrix
  • multilinear algebra

Published Papers (3 papers)

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Research

19 pages, 327 KiB  
Article
Stieltjes Property of Quasi-Stable Matrix Polynomials
by Xuzhou Zhan, Bohui Ban and Yongjian Hu
Mathematics 2022, 10(23), 4440; https://doi.org/10.3390/math10234440 - 24 Nov 2022
Cited by 1 | Viewed by 831
Abstract
In this paper, basing on the theory of matricial Hamburger moment problems, we establish the intrinsic connections between the quasi-stability of a monic or comonic matrix polynomial and the Stieltjes property of a rational matrix-valued function built from the even–odd split of the [...] Read more.
In this paper, basing on the theory of matricial Hamburger moment problems, we establish the intrinsic connections between the quasi-stability of a monic or comonic matrix polynomial and the Stieltjes property of a rational matrix-valued function built from the even–odd split of the original matrix polynomial. As applications of these connections, we obtain some new criteria for quasi-stable matrix polynomials and Hurwitz stable matrix polynomials, respectively. Full article
20 pages, 340 KiB  
Article
A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application
by Long-Sheng Liu, Qing-Wen Wang and Mahmoud Saad Mehany 
Mathematics 2022, 10(10), 1758; https://doi.org/10.3390/math10101758 - 21 May 2022
Cited by 12 | Viewed by 1481
Abstract
We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves η-Hermicity. We [...] Read more.
We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves η-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper. Full article
19 pages, 381 KiB  
Article
A Modified Conjugate Residual Method and Nearest Kronecker Product Preconditioner for the Generalized Coupled Sylvester Tensor Equations
by Tao Li, Qing-Wen Wang and Xin-Fang Zhang
Mathematics 2022, 10(10), 1730; https://doi.org/10.3390/math10101730 - 18 May 2022
Cited by 12 | Viewed by 1576
Abstract
This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on the Kronecker product approximations for solving the tensor [...] Read more.
This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on the Kronecker product approximations for solving the tensor equations. A theoretical analysis shows that the proposed method converges to an exact solution for any initial tensor at most finite steps in the absence round-off errors. Compared with a modified conjugate gradient method, the obtained numerical results illustrate that our methods perform much better in terms of the number of iteration steps and computing time. Full article
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