Determinants and inverses of weighted Loeplitz and weighted Foeplitz matrices and their applications in data encryption

被引：10

作者：

Meng, Qingyan ^{[1
]}

Zheng, Yanpeng ^{[2
]}

Jiang, Zhaolin ^{[1
]}

机构：

[1] Linyi Univ, Sch Math & Stat, Linyi 276000, Shandong, Peoples R China

[2] Linyi Univ, Sch Automat & Elect Engn, Linyi 276000, Shandong, Peoples R China

来源：

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2022年 / 68卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Weighted Loeplitz matrix; Weighted Foeplitz matrix; Lucas numbers; Fibonacci numbers; Determinant; Inverse; Data and image encryption; TOEPLITZ MATRICES; EIGENPAIRS; FIBONACCI;

D O I：

10.1007/s12190-022-01700-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the analytical determinants and inverses of n x n weighted Loeplitz and weighted Foeplitz matrices. We introduce the n x n weighted Loeplitz and weighted Foeplitz matrices and derive the analytical determinants and inverses of them by constructing the transformation matrices. Specifically, we can use the nth, (n + 1)st and (n + 2) th Fibonacci numbers to express the analytical inverse of the nxn weighted Loeplitz matrix which is sparse. We also present the analytical determiants and inverses of the n x n weighted Lankel and weighted Fankel matrices. Finally, we give two application examples of the main results in data and image encryption.

引用

页码：3999 / 4015

页数：17

共 50 条

[31] Weighted Symmetric Pivot Coordinates for Compositional Data with Geochemical Applications
Hron, Karel
Engle, Mark
Filzmoser, Peter
Fiserova, Eva
MATHEMATICAL GEOSCIENCES, 2021, 53 (04) : 655 - 674
[32] A weighted negative binomial Lindley distribution with applications to dispersed data
Bakouch, Hassan S.
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, 2018, 90 (03): : 2617 - 2642
[33] Applications of weighted association networks applied to compositional data in biology
Espinoza, Josh L.
Shah, Naisha
Singh, Suren
Nelson, Karen E.
Dupont, Chris L.
ENVIRONMENTAL MICROBIOLOGY, 2020, 22 (08) : 3020 - 3038
[34] A Weighted Skew-Logistic Distribution with Applications to Environmental Data
Cortes, Isaac
Reyes, Jimmy
Iriarte, Yuri A.
MATHEMATICS, 2024, 12 (09)
[35] Applications of threshold models and the weighted bootstrap for Hungarian precipitation data
László Varga
Pál Rakonczai
András Zempléni
Theoretical and Applied Climatology, 2016, 124 : 641 - 652
[36] Applications of threshold models and the weighted bootstrap for Hungarian precipitation data
Varga, Laszlo
Rakonczai, Pal
Zempleni, Andras
THEORETICAL AND APPLIED CLIMATOLOGY, 2016, 124 (3-4) : 641 - 652
[37] Weighted Moore-Penrose, Drazin, and group inverses of the Kronecker product A direct product B, and some applications
Linear Algebra and Its Applications, 1997, 250 : 39 - 50
[38] Weighted Moore-Penrose, Drazin, and group inverses of the Kronecker product A circle times B, and some applications
Wang, GR
LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 250 : 39 - 50
[39] New Weighted Lomax (NWL) Distribution with Applications to Real and Simulated Data
Alshanbari, Huda M.
Ijaz, Muhammad
Asim, Syed Muhammad
El-Bagoury, Abd Al-Aziz Hosni
Dar, Javid Gani
MATHEMATICAL PROBLEMS IN ENGINEERING, 2021, 2021
[40] On the Contaminated Weighted Exponential Distribution: Applications to Modeling Insurance Claim Data
Mahdavi, Abbas
Kharazmi, Omid
Contreras-Reyes, Javier E.
JOURNAL OF RISK AND FINANCIAL MANAGEMENT, 2022, 15 (11)

← 1 2 3 4 5 →