Research on Structured Matrices and Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 2955

Special Issue Editors


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Guest Editor
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Interests: structured matrix theory and applications; stability analysis of matrices and polynomials; interpolation and approximation of functions

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Guest Editor
School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, China
Interests: linear algebra; matrix theory; iterative methods; linear systems; numerical linear algebra; mathematical analysis; numerical analysis; functional analysis; MIMO communication; decoding; computational complexity; error analysis; interference suppression; lattice theory; mathematics computing; matrix inversion; recurrent neural nets; signal detection; vectors; continuous time systems; matrix algebra; optimal control; stability

Special Issue Information

Dear Colleagues,

A number of matrices with some structural symmetry (e.g., Hankel matrices, Toeplitz matrices, Vandermonde matrices, Bezout matrices) have been widely studied in the development of matrix theory. The research on these structured matrices includes matrix equations, matrix inequalities, matrix decompositions, matrix eigenvalue problems, fast matrix algorithms, linear systems of equations, tensor algebra, and spectral analysis, as well as their applications in enormous fields. This Special Issue will gather high-quality and original papers to present cutting-edge research regarding structured matrices, along with their applications in any area.

Prof. Dr. Yongjian Hu
Prof. Dr. Yimin Wei
Guest Editors

Manuscript Submission Information

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Keywords

  • structured matrices
  • symmetry
  • fast algorithm
  • matrix equations
  • matrix inequalities
  • matrix decompositions
  • linear systems of equations
  • eigenvalue problems
  • tensor algebra
  • spectral analysis

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Published Papers (2 papers)

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Research

15 pages, 301 KiB  
Article
Generalized Choi–Davis–Jensen’s Operator Inequalities and Their Applications
by Shih Yu Chang and Yimin Wei
Symmetry 2024, 16(9), 1176; https://doi.org/10.3390/sym16091176 - 9 Sep 2024
Cited by 1 | Viewed by 1146
Abstract
The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize [...] Read more.
The original Choi–Davis–Jensen’s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi–Davis–Jensen’s inequality by introducing a nonlinear map instead of a normalized linear map and generalize the concept of operator convex functions to include any continuous function defined within a compact region. Notably, operators can be matrices with structural symmetry, enhancing the scope and applicability of our results. The Stone–Weierstrass theorem and the Kantorovich function play crucial roles in the formulation and proof of these generalized Choi–Davis–Jensen’s inequalities. Furthermore, we demonstrate an application of this generalized inequality in the context of statistical physics. Full article
(This article belongs to the Special Issue Research on Structured Matrices and Applications)
12 pages, 857 KiB  
Article
Accurate Computations with Generalized Green Matrices
by Jorge Delgado, Guillermo Peña and Juan Manuel Peña
Symmetry 2024, 16(8), 1004; https://doi.org/10.3390/sym16081004 - 7 Aug 2024
Viewed by 986
Abstract
We consider generalized Green matrices that, in contrast to Green matrices, are not necessarily symmetric. In spite of the loss of symmetry, we show that they can preserve some nice properties of Green matrices. In particular, they admit a bidiagonal decomposition. Moreover, for [...] Read more.
We consider generalized Green matrices that, in contrast to Green matrices, are not necessarily symmetric. In spite of the loss of symmetry, we show that they can preserve some nice properties of Green matrices. In particular, they admit a bidiagonal decomposition. Moreover, for convenient parameters, the bidiagonal decomposition can be obtained efficiently and with high relative accuracy and it can also be used to compute all eigenvalues, all singular values, the inverse, and the solution of some linear system of equations with high relative accuracy. Numerical examples illustrate the high accuracy of the performed computations using the bidiagonal decompositions. Finally, nonsingular and totally positive generalized Green matrices are characterized. Full article
(This article belongs to the Special Issue Research on Structured Matrices and Applications)
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