Fault diagnosis of mechanical equipment is mainly based on the contact measurement and analysis of vibration signals. In some special working conditions, the non-contact fault diagnosis method represented by the measurement of acoustic signals can ma...
Symmetry plays a crucial role in the study of dual matrices and dual matrix group inverses. This paper is mainly divided into two parts. We present the definition of the spectral norm of a dual real matrix A^, (which is usually represented in the for...
We propose a new iterative method for solving a generalized Sylvester matrix equation A1XA2+A3XA4=E with given square matrices A1,A2,A3,A4 and an unknown rectangular matrix X. The method aims to construct a sequence of approximated solutions convergi...
We introduce a gradient iterative scheme with an optimal convergent factor for solving a generalized Sylvester matrix equation ∑i=1pAiXBi=F, where Ai,Bi and F are conformable rectangular matrices. The iterative scheme is derived from the gradient...
In this paper, we analyze the convergence problems of function g of Fourier series in Besov and generalized Zygmund norms using generalized Nörlund-Matrix (Np,qA) means of Fourier series. Convergence results are also compared by means of applications...
We consider a variant of the online semi-definite programming problem (OSDP). Specifically, in our problem, the setting of the decision space is a set of positive semi-definite matrices constrained by two norms in parallel: the L∞ norm to the d...
In the present paper, an iterative algorithm is proposed for solving the generalized (P,Q)-reflexive solution group of a system of quaternion matrix equations ∑l=1M(AlsXlBls+ClsXl˜Dls)=Fs,s=1,2,…,N. A generalized (P,Q)-reflexive solu...
This paper proposes a class of randomized Kaczmarz and Gauss–Seidel-type methods for solving the matrix equation AXB=C, where the matrices A and B may be either full-rank or rank deficient and the system may be consistent or inconsistent. These...
Traditional image denoising algorithms obtain prior information from noisy images that are directly based on low rank matrix restoration, which pays little attention to the nonlocal self-similarity errors between clear images and noisy images. This p...
The energy E(G) of a graph G is the sum of the absolute values of its adjacency matrix. In contrast, the trace norm of a digraph Q, which is the sum of the singular values of the corresponding adjacency matrix, is the oriented version of the energy o...
The concept of the energy of a graph has been widely explored in the field of mathematical chemistry and is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of a hypergraph is the trace norm of its conn...
Low-Rank Tensor Recovery (LRTR), the higher order generalization of Low-Rank Matrix Recovery (LRMR), is especially suitable for analyzing multi-linear data with gross corruptions, outliers and missing values, and it attracts broad attention in the fi...
It is well known that the position of the Jacobian matrix spectrum in the left-half complex plane provides the local asymptotic stability of a nonlinear dynamical system, but it is also well known that for large matrices, computing its eigenvalues ju...
More recently, the ability of the coprime array to yield large array apertures and high degrees of freedom in comparison with the uniform linear array (ULA) has drawn an enormous amount of attention. In light of this, we propose a low-rank matrix com...
The solvability conditions, symmetric solutions, and antisymmetric solutions of matrix equations AX=B are important research topics in matrix theory. As a higher-order generalization of matrices, tensors have made the research on solving tensor equat...
This paper considers the problem of robust bearing-only source localization in impulsive noise with symmetric α-stable distribution based on the Lp-norm minimization criterion. The existing Iteratively Reweighted Pseudolinear Least-Squares (IRPLS) me...
The data presented here contain information on cheating behavior from experiments and general self-reported attitudes related to honesty-related social norms and trust, together with individual-level demographic variables. Our sample included 493 uni...
The present paper attempts to investigate the problem of robust H ∞ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability...
This paper investigates new solution sets for the Yang–Baxter-like (YB-like) matrix equation involving constant entries or rational functional entries over complex numbers. Towards this aim, first, we introduce and characterize an essential cla...
This study introduces a novel generalization: the generalized geometric Frank matrix, which extends the classical Frank matrix and its known variants. We systematically examine its algebraic structure, providing detailed analyses of its factorization...
We consider general higher-order matrix elliptic differential–difference operators in arbitrary domains with small variable translations in lower-order terms. The operators are introduced by means of general higher-order quadratic forms on arbi...
In recent years, there has been a substantial surge in the application of image watermarking, which has evolved into an essential tool for identifying multimedia material, ensuring security, and protecting copyright. Singular value decomposition (SVD...
Fuzzy clustering is widely used in business, biology, geography, coding for the internet and more. A single-valued neutrosophic set is a generalized fuzzy set, and its clustering algorithm has attracted more and more attention. An equivalence matrix...
In this work, we introduce a mixed type of quadratic-additive (QA) functional equation and obtain its general solution. The objective of this work is to investigate the Ulam–Hyers stability of this quadratic-additive (QA) functional equation in...
Hyperspectral image (HSI) change detection (CD) is an important technology for identifying surface changes using multi-temporal HSIs. Nevertheless, the high dimensionality of HSIs presents significant challenges for CD tasks, including issues such as...
We derive a conjugate-gradient type algorithm to produce approximate least-squares (LS) solutions for an inconsistent generalized Sylvester-transpose matrix equation. The algorithm is always applicable for any given initial matrix and will arrive at...
The Non-negative Matrix Factorization (NMF) is a popular technique for intelligent systems, which can be widely used to decompose a nonnegative matrix into two factor matrices: a basis matrix and a coefficient one, respectively. The main objective of...
The semantic social network is a complex system composed of nodes, links, and documents. Traditional semantic social network community detection algorithms only analyze network data from a single view, and there is no effective representation of sema...
This paper proposes a fast direction of arrival (DOA) estimation method based on positive incremental modified Cholesky decomposition atomic norm minimization (PI-CANM) for augmented coprime array sensors. The approach incorporates coprime sampling o...
The most popular iterative methods for solving nonsymmetric linear systems are Krylov methods. Recently, an optimal Quasi-ORthogonal (Q-OR) method was introduced, which yields the same residual norms as the Generalized Minimum Residual (GMRES) method...
The diagonal dominance property has been applied in many different ways and has proven to be very useful in various research areas. Its generalization, also known under the name H-matrix property, can be applied and produce significant benefits in ec...
The main topic in this article is to define and examine new sequence spaces bs(F^(s,r)) and cs(F^(s,r))), where F^(s,r) is generalized difference Fibonacci matrix in which s,r∈R\0. Some algebric properties including some inclusion relations, lin...
Hyperspectral image (HSI) quality is generally degraded by diverse noise contamination during acquisition, which adversely impacts subsequent processing performance. Current techniques predominantly rely on nuclear norms and low-rank matrix approxima...
The low-rank and sparse decomposition model has been favored by the majority of hyperspectral image anomaly detection personnel, especially the robust principal component analysis(RPCA) model, over recent years. However, in the RPCA model, ℓ0 o...
Let p→∈(0,∞)n be an exponent vector and A be a general expansive matrix on Rn. Let HAp→(Rn) be the anisotropic mixed-norm Hardy spaces associated with A defined via the non-tangential grand maximal function. In this article, using the known atomic ch...
The forthcoming property of this manuscript is its calculating of the goal of norms and lower bounds of matrix operators taken from the weighted sequence space ℓp(w) onto a novel one defined in the present article as the generalized Fibonacci w...
Based on low-rank matrix reconstruction theory, this paper proposes a joint DOD and DOA estimation method for coherent targets with bistatic coprime array MIMO radar. Unlike the conventional vectorization, the proposed method processed the coprime ar...
Transformer-based models have achieved remarkable success across various AI tasks, but their growing complexity has led to significant computational and memory demands. While most optimization efforts have focused on linear operations such as matrix...
In the present paper, we propose to study generalized weighted backward shifts BB over non-Archimedean c0(N) spaces; here, B=(bij) is an upper triangular matrix with supi,j|bij|<∞. We investigate the sypercyclic and hypercyclic properties of...
We generalize the property of complex numbers to be closely related to Euclidean circles by constructing new classes of complex numbers which in an analogous sense are closely related to semi-antinorm circles, ellipses, or functionals which are homog...
In real-world scenarios, images may be affected by additional noise during compression and transmission, which interferes with postprocessing such as image segmentation and feature extraction. Image noise can also be induced by environmental variable...
In recent years, with the development of compressed sensing theory, sparse representation methods have been concerned by many researchers. Sparse representation can approximate the original image information with less space storage. Sparse representa...
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 inst...
Multi-source heterogeneous data has been widely adopted in developing artificial intelligence systems in recent years. In real-world scenarios, raw multi-source data are generally unlabeled and inherently contain multi-view noise and feature redundan...
Aimed at the issue of estimating the fault component from a noisy observation, a novel detection approach based on augmented Huber non-convex penalty regularization (AHNPR) is proposed. The core objectives of the proposed method are that (1) it estim...
The primary focus of this research study is in the development of an effective hybrid matrix method to solve a class of nonlinear systems of equations of fractional order arising in the modeling of autocatalytic chemical reaction problems. The fracti...
Aiming at multi-agent interest demands and environmental benefits, a distributionally robust game-theoretic optimization algorithm based on a green certificate–carbon trading mechanism is proposed for uncertain microgrids. At first, correlated...
The paper is a survey of the recent results of the author on the perturbations of matrices. A part of the results presented in the paper is new. In particular, we suggest a bound for the difference of the determinants of two matrices which refines th...
We introduce a qϱ-implicit contractive condition by an implicit relation on relational quasi partial metric spaces and establish new (unique) fixed point results and periodic point results based on it. We justify the results by two suitable examples...
We discuss a pair of nonlinear matrix equations (NMEs) of the form X=R1+∑i=1kAi*F(X)Ai, X=R2+∑i=1kBi*G(X)Bi, where R1,R2∈P(n), Ai,Bi∈M(n), i=1,⋯,k, and the operators F,G:P(n)→P(n) are continuous in the trace norm. We go through the necessary criteria...
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