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Journal articles on the topic 'Method of matrices'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Mechal Fheed Alslman, Nassr Aldin Ide, Ahmad Zakzak, Mechal Fheed Alslman, Nassr Aldin Ide, Ahmad Zakzak. "Building matrixes of higher order to achieve the special commutative multiplication and its applications in cryptography: بناء مصفوفات تبديلية من مراتب عليا وتطبيقاتها في التشفير". Journal of natural sciences, life and applied sciences 5, № 3 (2021): 16–1. http://dx.doi.org/10.26389/ajsrp.c260521.

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In this paper, we introduce a method for building matrices that verify the commutative property of multiplication on the basis of circular matrices, as each of these matrices can be divided into four circular matrices, and we can also build matrices that verify the commutative property of multiplication from higher order and are not necessarily divided into circular matrices. Using these matrixes, we provide a way to securely exchange a secret encryption key, which is a square matrix, over open communication channels, and then use this key to exchange encrypted messages between two sides or tw

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2

LI, Lei. "A Recursive Test for Judging M-Matrices and H-Matrices." Information 28, no. 1 (2025): 23–31. https://doi.org/10.47880/inf2801-02.

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A n × n complex matrix A is called H-matrix if its comparison matrix is a M-matrix. H-matrix and M-matrix are two important classes of special matrices which often appear in fields of system control and scientific computation. Many application problems are needed to judge whether a known complex matrix A is a H-matrix or not (Or equivalently, judge whether its comparison matrix M(A) is a M-matrix or not). Some iterative methods and direct methods have been presented in previous researches separately. But it is difficult to predict necessary number of iterations before ending these iterative me

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3

Wu, Shi-Liang, and Yu-Jun Liu. "A New Version of the Accelerated Overrelaxation Iterative Method." Journal of Applied Mathematics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/725360.

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Hadjidimos (1978) proposed a classical accelerated overrelaxation (AOR) iterative method to solve the system of linear equations, and discussed its convergence under the conditions that the coefficient matrices are irreducible diagonal dominant,L-matrices, and consistently orders matrices. In this paper, a new version of the AOR method is presented. Some convergence results are derived when the coefficient matrices are irreducible diagonal dominant,H-matrices, symmetric positive definite matrices, andL-matrices. A relational graph for the new AOR method and the original AOR method is presented

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4

Kudin, V. I. "A method of pseudobasis matrices." Reports of the National Academy of Sciences of Ukraine, no. 8 (August 25, 2014): 53–56. http://dx.doi.org/10.15407/dopovidi2014.08.053.

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5

Dahl, Geir. "A method for approximating symmetrically reciprocal matrices by transitive matrices." Linear Algebra and its Applications 403 (July 2005): 207–15. http://dx.doi.org/10.1016/j.laa.2005.02.002.

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6

Fülöp, János. "A method for approximating pairwise comparison matrices by consistent matrices." Journal of Global Optimization 42, no. 3 (2008): 423–42. http://dx.doi.org/10.1007/s10898-008-9303-0.

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7

Devasahayam, Joseph Jeyakumar, Shanmathi Boominathan, Bahulayan Smitha Parappurathu, Vinurajkumar Sekar, Murali Mohanan, and Mariselvam Muthuraj. "Hermitan matrices based malicious cognitive radio detection and bayesian method for detecting primary user emulation attack." Hermitan matrices based malicious cognitive radio detection and bayesian method for detecting primary user emulation attack 30, no. 2 (2023): 956–64. https://doi.org/10.11591/ijeecs.v30.i2.pp956-964.

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Cognitive radio (CR) is a facilitating technology to efficiently deal with the spectrum scarceness, and it will significantly enhance the spectrum deployment of upcoming wireless transmission method. Security is a significant concern, although not well tackle in cognitive radio networks (CRN). In CR networks, this approach regard as a security issue happen from primary user emulation attack (PUEA). A PUEA attacker forwards an emulated primary signal and defraud the CR users to avoid them from accessing spectrum holes. Here, we introduce a Hermitan matrices based malicious cognitive radio (CMCR

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8

Fedotov, Alexander, and Frédéric Klopp. "A complex WKB method for adiabatic problems." Asymptotic Analysis 27, no. 3-4 (2001): 219–64. https://doi.org/10.3233/asy-2001-452.

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This work is devoted to a new version of the complex WKB method suited for adiabatic perturbations of one‐dimensional periodic Schrödinger operators. Therefore, we introduce an additional parameter, and it is this parameter (and not the variable of the equation) that will become complex. This naturally leads to canonical domains where we construct solutions of the Schrödinger equation with a standard asymptotic behavior. These can be used to compute the asymptotics of the exponentially small coefficients of transfer matrices (e.g., scattering matrices, monodromy matrices, etc.). We give an exa

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9

Ikramov, Kh D. "On the bisection method for normal matrices." Доклады Академии наук 485, no. 6 (2019): 659–61. http://dx.doi.org/10.31857/s0869-56524856659-661.

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10

Dai, Li-fang, Mao-lin Liang, and Yong-hong Shen. "An Iterative Method for the Least-Squares Problems of a General Matrix Equation Subjects to Submatrix Constraints." Journal of Applied Mathematics 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/697947.

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An iterative algorithm is proposed for solving the least-squares problem of a general matrix equation∑i=1t‍MiZiNi=F, whereZi(i=1,2,…,t) are to be determined centro-symmetric matrices with given central principal submatrices. For any initial iterative matrices, we show that the least-squares solution can be derived by this method within finite iteration steps in the absence of roundoff errors. Meanwhile, the unique optimal approximation solution pair for given matricesZ~ican also be obtained by the least-norm least-squares solution of matrix equation∑i=1t‍MiZ-iNi=F-, in whichZ-i=Zi-Z~i, F-=F-∑i

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11

SHIMAZAKI, Yoji. "Frontal-skyline method for unsymmetric matrices." Doboku Gakkai Ronbunshu, no. 356 (1985): 101–8. http://dx.doi.org/10.2208/jscej.1985.356_101.

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12

Pearson, D. B., and P. L. I. Skelton. "The Inverse Method for Transfer Matrices." Journal of the London Mathematical Society s2-40, no. 3 (1989): 476–89. http://dx.doi.org/10.1112/jlms/s2-40.3.476.

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13

Evans, D. J., and C. Li. "Sor method andp-cyclic matrices (I)." International Journal of Computer Mathematics 36, no. 1-2 (1990): 57–76. http://dx.doi.org/10.1080/00207169008803911.

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14

Evans, D. J., and Changjun Li. "Sor method andP-cyclic matrices (II)." International Journal of Computer Mathematics 37, no. 3-4 (1990): 239–50. http://dx.doi.org/10.1080/00207169008803952.

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15

Kotakemori, Hisashi, Hiroshi Niki, and Naotaka Okamoto. "Accelerated iterative method for Z-matrices." Journal of Computational and Applied Mathematics 75, no. 1 (1996): 87–97. http://dx.doi.org/10.1016/s0377-0427(96)00061-1.

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16

Hacon, Derek. "Jacobi’s Method for Skew-Symmetric Matrices." SIAM Journal on Matrix Analysis and Applications 14, no. 3 (1993): 619–28. http://dx.doi.org/10.1137/0614043.

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17

Kanzieper, E. "Random matrices and the replica method." Nuclear Physics B 596, no. 3 (2001): 548–66. http://dx.doi.org/10.1016/s0550-3213(00)00749-5.

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18

Halász, Miklós Adam. "Random matrices and the Glasgow method." Nuclear Physics A 642, no. 1-2 (1998): c324—c329. http://dx.doi.org/10.1016/s0375-9474(98)00532-6.

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19

Jiang, Er-xiong. "QL method for symmetric tridiagonal matrices." Journal of Shanghai University (English Edition) 8, no. 4 (2004): 369–77. http://dx.doi.org/10.1007/s11741-004-0047-x.

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20

Rao, N. Raj, and Alan Edelman. "The Polynomial Method for Random Matrices." Foundations of Computational Mathematics 8, no. 6 (2007): 649–702. http://dx.doi.org/10.1007/s10208-007-9013-x.

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21

Robert, Leonel, and Luis Santiago. "Finite sections method for Hessenberg matrices." Journal of Approximation Theory 123, no. 1 (2003): 68–88. http://dx.doi.org/10.1016/s0021-9045(03)00067-4.

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22

Kudin, V. I. "The method of permissible basis matrices." Reports of the National Academy of Sciences of Ukraine, no. 9 (September 25, 2014): 44–48. http://dx.doi.org/10.15407/dopovidi2014.09.044.

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23

Huckle, Thomas. "The Arnoldi Method for Normal Matrices." SIAM Journal on Matrix Analysis and Applications 15, no. 2 (1994): 479–89. http://dx.doi.org/10.1137/s0895479891219964.

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24

Chen, Zhilong, Peng Wang, and Detong Zhu. "Approximation Conjugate Gradient Method for Low-Rank Matrix Recovery." Symmetry 16, no. 5 (2024): 547. http://dx.doi.org/10.3390/sym16050547.

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Large-scale symmetric and asymmetric matrices have emerged in predicting the relationship between genes and diseases. The emergence of large-scale matrices increases the computational complexity of the problem. Therefore, using low-rank matrices instead of original symmetric and asymmetric matrices can greatly reduce computational complexity. In this paper, we propose an approximation conjugate gradient method for solving the low-rank matrix recovery problem, i.e., the low-rank matrix is obtained to replace the original symmetric and asymmetric matrices such that the approximation error is the

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25

Hu, Jingdan. "A Method for Constructing Concentration Boolean Matrix." Scientific Journal of Intelligent Systems Research 7, no. 1 (2025): 53–60. https://doi.org/10.54691/93qrxn37.

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Attribute reduction is a significant problem in rough set theory. It has been widely applied in fields such as pattern recognition and data mining. The research on attribute reduction algorithms based on discernibility matrices has attracted continuous attention from scholars. This paper proposes a method for constructing concentration Boolean matrices. By investigating the row sums of Boolean matrices, multiple discernibility elements can be simultaneously removed. Through case studies, it is demonstrated that this method can identify all minimal discernibility elements without the need for e

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26

Stanimirović, Predrag, Marko Miladinović, Igor Stojanović, and Sladjana Miljković. "Application of the partitioning method to specific Toeplitz matrices." International Journal of Applied Mathematics and Computer Science 23, no. 4 (2013): 809–21. http://dx.doi.org/10.2478/amcs-2013-0061.

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Abstract We propose an adaptation of the partitioning method for determination of theMoore-Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant reduction in the computational time required to calculate the Moore-Penrose invers

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27

Diţă, Petre. "Complex Hadamard Matrices from Sylvester Inverse Orthogonal Matrices." Open Systems & Information Dynamics 16, no. 04 (2009): 387–405. http://dx.doi.org/10.1142/s1230161209000281.

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A novel method to obtain parametrizations of complex inverse orthogonal matrices is provided. These matrices are natural generalizations of complex Hadamard matrices which depend on complex parameters. The method we use is via doubling the size of inverse complex conference matrices. When the free parameters take values on the unit circle the inverse orthogonal matrices transform into complex Hadamard matrices, and in this way we find new parametrizations of Hadamard matrices for dimensions n = 8, 10, and 12.

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28

Serbenyuk, Symon. "Matrix analysis: method simplifications." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 15 (December 30, 2023): 15–24. http://dx.doi.org/10.24917/20809751.15.2.

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This paper is devoted to explanations of calculation techniques in matrix theory under its teaching and learning, focusing on the notion of matrices and algebraic operations on matrices. Some attention is given to recommendations for teaching of determinants. A purpose of the main part of the article is to provide recommendations for lecturers to help them in teaching matrix theory, in a way that will enable for students to understand the content studied in a short time. Auxiliary schemes, short notations, and recommendations are given.

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29

Zaikov, K. D., A. S. Anikin, and K. A. Yarkov. "Methods for calculating scattering matrices of analog path of active phased array antennas." Ural Radio Engineering Journal 6, no. 2 (2022): 205–21. http://dx.doi.org/10.15826/urej.2022.6.2.005.

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The paper is devoted to determining the optimal method for calculating the cascade connection of scattering matrices according to the criterion of the least computational complexity and the highest accuracy. The analysis is carried out for several methods: the block N-matrices method, the block T-matrices method, and the method of free and coupled ports. The article presents a numerical analysis of the accuracy of the presented methods, as well as numerical indicators of computational complexity.

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30

Enyew, Tesfaye Kebede, Gurju Awgichew, Eshetu Haile, and Gashaye Dessalew Abie. "Second-refinement of Gauss-Seidel iterative method for solving linear system of equations." Ethiopian Journal of Science and Technology 13, no. 1 (2020): 1–15. http://dx.doi.org/10.4314/ejst.v13i1.1.

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Although large and sparse linear systems can be solved using iterative methods, its number of iterations is relatively large. In this case, we need to modify the existing methods in order to get approximate solutions in a small number of iterations. In this paper, the modified method called second-refinement of Gauss-Seidel method for solving linear system of equations is proposed. The main aim of this study was to minimize the number of iterations, spectral radius and to increase rate of convergence. The method can also be used to solve differential equations where the problem is transformed

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31

Práger, Milan. "An iterative method of alternating type for systems with special block matrices." Applications of Mathematics 36, no. 1 (1991): 72–78. http://dx.doi.org/10.21136/am.1991.104444.

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32

Tafrikan, Mohammad, and Mohammad Ghani. "Iterative Method of Thomas Algorithm on The Case Study of Energy Equation." Postulat : Jurnal Inovasi Pendidikan Matematika 3, no. 1 (2022): 14. http://dx.doi.org/10.30587/postulat.v3i1.4346.

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Implicit method is one of the finite difference method and is widely used for discretization some of ordinary or partial differential equations, such like: advection equation, heat transfer equation, burger equation, and many others. Implicit method is unconditionally stable and has been proved with the approximation of Von-Neumann stability criterion. Actually, implicit method is always identical to block matrices (tri-diagonal matrices or penta-diagonal matrices). These matrices can be solved numerically by Thomas algorithm including Gauss elimination using pivot or not, backward or forward

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33

Turan Dincel, Arzu, Sadiye Nergis Tural Polat, and Pelin Sahin. "Hermite Wavelet Method for Nonlinear Fractional Differential Equations." Fractal and Fractional 7, no. 5 (2023): 346. http://dx.doi.org/10.3390/fractalfract7050346.

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Nonlinear fractional differential equations (FDEs) constitute the basis for many dynamical systems in various areas of engineering and applied science. Obtaining the numerical solutions to those nonlinear FDEs has quickly gained importance for the purposes of accurate modelling and fast prototyping among many others in recent years. In this study, we use Hermite wavelets to solve nonlinear FDEs. To this end, utilizing Hermite wavelets and block-pulse functions (BPF) for function approximation, we first derive the operational matrices for the fractional integration. The novel contribution provi

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34

Sobamowo, M. G. "On the Extension of Sarrus’ Rule to n×n (n>3) Matrices: Development of New Method for the Computation of the Determinant of 4×4 Matrix." International Journal of Engineering Mathematics 2016 (December 5, 2016): 1–14. http://dx.doi.org/10.1155/2016/9382739.

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The determinant of a matrix is very powerful tool that helps in establishing properties of matrices. Indisputably, its importance in various engineering and applied science problems has made it a mathematical area of increasing significance. From developed and existing methods of finding determinant of a matrix, basketweave method/Sarrus’ rule has been shown to be the simplest, easiest, very fast, accurate, and straightforward method for the computation of the determinant of 3 × 3 matrices. However, its gross limitation is that this method/rule does not work for matrices larger than 3 × 3 and

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35

Horáček, Jaroslav, Milan Hladík, and Josef Matějka. "Determinants of Interval Matrices." Electronic Journal of Linear Algebra 33 (May 16, 2018): 99–112. http://dx.doi.org/10.13001/1081-3810.3719.

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In this paper we shed more light on determinants of real interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both relative and absolute approximation is proved. Next, methods computing verified enclosures of interval determinants and their possible combination with preconditioning are discussed. A new method based on Cramer's rule was designed. It returns similar results to the state-of-the-art method, however, it is less consuming regarding computational time. Other met

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36

Razzaghi, Mohsen. "A Schur method for the solution of the matrix Riccati equation." International Journal of Mathematics and Mathematical Sciences 20, no. 2 (1997): 335–38. http://dx.doi.org/10.1155/s0161171297000446.

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This paper is concerned with an analytic solution of the finite-time matrix Riccati equation. The solution to the Riccati equation is given in terms of multiple of two matrices. These matrices are found using a Schur-type decomposition for Hamiltonian matrices. Simple examples illustrating the method are presented.

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37

Theeracheep, Siraphob, and Jaruloj Chongstitvatana. "Multiplication of medium-density matrices using TensorFlow on multicore CPUs." Tehnički glasnik 13, no. 4 (2019): 286–90. http://dx.doi.org/10.31803/tg-20191104183930.

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Matrix multiplication is an essential part of many applications, such as linear algebra, image processing and machine learning. One platform used in such applications is TensorFlow, which is a machine learning library whose structure is based on dataflow programming paradigm. In this work, a method for multiplication of medium-density matrices on multicore CPUs using TensorFlow platform is proposed. This method, called tbt_matmul, utilizes TensorFlow built-in methods tf.matmul and tf.sparse_matmul. By partitioning each input matrix into four smaller sub-matrices, called tiles, and applying an

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38

Gutiérrez-Gutiérrez, Jesús, Xabier Insausti, and Marta Zárraga-Rodríguez. "Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing." Mathematics 8, no. 4 (2020): 582. http://dx.doi.org/10.3390/math8040582.

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In this paper, we combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition to give a parameter estimation method for any perturbed vector autoregressive (VAR) or vector moving average (VMA) process, when we only know a perturbed version of the sequence of correlation matrices of the process. In order to combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition, we first need to generalize a known result on the Cholesky decomposition of Toeplitz matrices to perturbed block Toeplitz matrices.

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39

LOMBARDINI, RICHARD, and BILL POIRIER. "PARALLEL SUBSPACE ITERATION METHOD FOR THE SPARSE SYMMETRIC EIGENVALUE PROBLEM." Journal of Theoretical and Computational Chemistry 05, no. 04 (2006): 801–18. http://dx.doi.org/10.1142/s0219633606002738.

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A new parallel iterative algorithm for the diagonalization of real sparse symmetric matrices is introduced, which uses a modified subspace iteration method. A novel feature is the preprocessing of the matrix prior to iteration, which allows for a natural parallelization resulting in a great speedup and scalability of the method with respect to the number of compute nodes. The method is applied to Hamiltonian matrices of model systems up to six degrees of freedom, represented in a truncated Weyl–Heisenberg wavelet (or "weylet") basis developed by one of the authors (Poirier). It is shown to acc

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40

Kane, K., and B. J. Torby. "The Extended Modal Reduction Method Applied to Rotor Dynamic Problems." Journal of Vibration and Acoustics 113, no. 1 (1991): 79–84. http://dx.doi.org/10.1115/1.2930159.

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In this paper, the existing Modal Reduction Method, which was developed to handle symmetric mass and stiffness matrices, is extended utilizing state-space formulation to handle nonsymmetric mass, damping, and stiffness matrices. These type of matrices typically accompany rotor dynamic problems since journal bearings supporting the rotor have nonsymmetric stiffness and damping characteristics. The purpose of modal reduction is to eliminate unimportant modes and degrees of freedom from the analytical model after they are found, so that further numerical analysis can be accelerated. The reduction

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41

KONONOV, SERGEY. "ON THE EXISTENCE, METHOD OF CONSTRUCTION AND SOME PROPERTIES OF (N - 2)-STRUCTURED MATRICES GENERATING BIJECTIVE TRANSFORMATIONS." Computational Nanotechnology 9, no. 1 (2022): 93–105. http://dx.doi.org/10.33693/2313-223x-2022-9-1-93-105.

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The article considers a new type of matrices that define bijective coordinate-threshold mappings - (n - 2)- structured matrices. It is proved that different matrices define different transformations, all (n - 2)-structured matrices of order 4 are described. For an arbitrary n ∈ ℕ, n classes of (n - 2)-structured matrices are specified, it is proved that the transformations specified by these matrices generate the group S2 S2n - 1. It is shown that the matrix transposed to the given one generates the inverse transformation.

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42

XING, YUFENG, BO LIU, and GUANG LIU. "A DIFFERENTIAL QUADRATURE FINITE ELEMENT METHOD." International Journal of Applied Mechanics 02, no. 01 (2010): 207–27. http://dx.doi.org/10.1142/s1758825110000470.

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This paper studies the differential quadrature finite element method (DQFEM) systematically, as a combination of differential quadrature method (DQM) and standard finite element method (FEM), and formulates one- to three-dimensional (1-D to 3-D) element matrices of DQFEM. It is shown that the mass matrices of C 0 finite element in DQFEM are diagonal, which can reduce the computational cost for dynamic problems. The Lagrange polynomials are used as the trial functions for both C 0 and C 1 differential quadrature finite elements (DQFE) with regular and/or irregular shapes, this unifies the selec

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43

Soleymani, F., and Predrag S. Stanimirović. "A Higher Order Iterative Method for Computing the Drazin Inverse." Scientific World Journal 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/708647.

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A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper.

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44

Jin, Yueting. "Calculation of Two Classes of Determinants by Reduction Method and Order-Increase Method." Theoretical and Natural Science 106, no. 1 (2025): 15–23. https://doi.org/10.54254/2753-8818/2025.22744.

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This paper explores two systematic approaches for computing determinants of structured matrices using Laplace Expansion. The reduction (recursion) method leverages recursive expansion to decompose high-order determinants into lower-order counterparts, exploiting structural repetition. This method simplifies complex calculations by iteratively applying Laplace Expansion. The order-increase (edge) method strategically augments matrices with auxiliary rows and columns to transform them into solvable forms. Examples include converting a -order determinant into an upper triangular matrix and extend

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45

Cherng, An-Pan, and M. K. Abdelhamid. "On the Symmetrization of Asymmetric Finite Dimensional Linear Dynamic Systems." Journal of Vibration and Acoustics 115, no. 4 (1993): 417–21. http://dx.doi.org/10.1115/1.2930366.

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A linear dynamic system with constant mass, and asymmetric damping and stiffness coefficient matrices, may be transformed to a symmetric system where all coefficient matrices are symmetric. This transformation makes it possible to take advantage of the well-developed theories that use the properties of the symmetric coefficient matrices. Some previous studies have suggested a decomposition method associated with rank checking of a rectangular matrix to determine if such transformations exist. However, these methods were only applicable to coefficient matrices with distinct eigenvalues, and the

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46

Guo, Han, Jun Hu, Hanru Shao, and Zaiping Nie. "Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations." International Journal of Antennas and Propagation 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/756259.

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Hierarchical (H-) matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE-) based computational electromagnetics,H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solveH-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure o

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47

Corr, Brian P., Tomasz Popiel, and Cheryl E. Praeger. "Nilpotent-independent sets and estimation in matrix algebras." LMS Journal of Computation and Mathematics 18, no. 1 (2015): 404–18. http://dx.doi.org/10.1112/s146115701500008x.

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Efficient methods for computing with matrices over finite fields often involve randomised algorithms, where matrices with a certain property are sought via repeated random selection. Complexity analyses for such algorithms require knowledge of the proportion of relevant matrices in the ambient group or algebra. We introduce a method for estimating proportions of families $N$ of elements in the algebra of all $d\times d$ matrices over a field of order $q$, where membership of a matrix in $N$ depends only on its ‘invertible part’. The method is based on the availability of estimates for proporti

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48

Bellfkih, El Mehdi, Said Nouh, Imrane Chems Eddine Idrissi, Khalid Louartiti, and Jamal Mouline. "Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices." Computational and Mathematical Methods 2023 (December 30, 2023): 1–8. http://dx.doi.org/10.1155/2023/5951901.

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In this paper, we present an innovative approach for the discovery of involutory maximum distance separable (MDS) matrices over finite fields F2q, derived from MDS self-dual codes, by employing a technique based on genetic algorithms. The significance of involutory MDS matrices lies in their unique properties, making them valuable in various applications, particularly in coding theory and cryptography. We propose a genetic algorithm-based method that efficiently searches for involutory MDS matrices, ensuring their self-duality and maximization of distances between code words. By leveraging the

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Zhou, Shihua, Pinyan He, and Nikola Kasabov. "A Dynamic DNA Color Image Encryption Method Based on SHA-512." Entropy 22, no. 10 (2020): 1091. http://dx.doi.org/10.3390/e22101091.

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This paper presents a dynamic deoxyribonucleic acid (DNA) image encryption based on Secure Hash Algorithm-512 (SHA-512), having the structure of two rounds of permutation–diffusion, by employing two chaotic systems, dynamic DNA coding, DNA sequencing operations, and conditional shifting. We employed the SHA-512 algorithm to generate a 512-bit hash value and later utilized this value with the natural DNA sequence to calculate the initial values for the chaotic systems and the eight intermittent parameters. We implemented a two-dimensional rectangular transform (2D-RT) on the permutation. We use

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Yuan, Rui, Yuexing Han, and Xi Lu. "Nonlinear Random Matrix-Based Intelligent Management Model for Swimming Place Waters." Mathematical Problems in Engineering 2022 (June 27, 2022): 1–12. http://dx.doi.org/10.1155/2022/7601021.

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In this paper, a nonlinear random matrix approach is used to analyze the management of swimming place waters, and in this way, an intelligent management model is designed and applied to the actual swimming place waters management. Firstly, some basic small deviation results of the random matrix are presented. Then, several types of small deviation inequalities are obtained for the maximum eigenvalues of independent stochastic semi-positive definite (PSD) matrices. These small deviation inequalities are independent of the matrix dimension, and the results apply to high-dimensional and even infi

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