In this work, combined matrices of tridiagonal Toeplitz matrices are studied. The combined matrix is known as the Relative Gain Array in control theory. In particular, given a real tridiagonal Toeplitz matrix of order n, the characterization of its c...
Toeplitz matrix–vector products are used in many digital signal processing applications. Direct methods for calculating such products require
Nonlocal circumstances in genetic engineering are crucial as they pertain to the understanding of genetic material. When these conditions are associated with differential integral equations, particularly concerning the time variable, they yield compr...
Conventional acoustic velocity-independent direction of arrival (DOA) estimation models have limited measurement ranges and low degrees of freedom. This paper proposes an omnidirectional DOA estimation model based on improved Toeplitz matrix reconstr...
With the explosive growth of voice information interaction, there is an urgent need for safe and effective compression transmission methods. In this paper, compressive sensing is used to realize the compression and encryption of speech signals. First...
Let Cn, Tn and Hn denote almost circulant, Cauchy-ToeplitZ and Cauchy-Hankel matrices, respectively. We find some upper bounds for \(\ell_p\) matrix norm and \(\ell_p\) operator norm of this matrices. Moreover, we give some results for Kronecker prod...
The Toeplitz matrix reconstruction methods are capable of resolving coherent signals, playing a crucial role in the direction-of-arrival (DOA) estimation of acoustic sources. However, the decoherence processing sacrifices the array aperture and furth...
In this paper, a Toeplitz construction method based on eigenvalues and eigenvectors is proposed to combine with traditional denoising algorithms, including fractional low-order moment (FLOM), phased fractional low-order moment (PFLOM), and correntrop...
This paper conducts a rigorous study on the spectral properties and operator-space distances of perturbed Dirichlet–Neumann tridiagonal (PDNT) Toeplitz matrices, with emphasis on their asymptotic behaviors. We establish explicit closed-form sol...
Coprime arrays have shown potential advantages for direction-of-arrival (DOA) estimation by increasing the number of degrees-of-freedom in the difference coarray domain with fewer physical sensors. In this paper, a new DOA estimation algorithm for co...
Privacy amplification is an indispensable procedure for key generation in the quantum key distribution system and the physical layer key distribution system. In this paper, we propose a high-speed privacy amplification algorithm that saves hardware m...
The purpose of this work is to study the efficient numerical solvers for time-dependent conservative space fractional diffusion equations. Specifically, for the discretized Toeplitz-like linear system, we aim to study efficient preconditioning based...
In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explic...
Foeplitz and Loeplitz matrices are Toeplitz matrices with entries being Fibonacci and Lucas numbers, respectively. In this paper, explicit expressions of determinants and inverse matrices of Foeplitz and Loeplitz matrices are studied. Specifically, t...
We present an algebraic framework for constructing challenge–response authentication protocols based on powers of non-diagonalizable matrices over finite fields. The construction relies on upper triangular Toeplitz matrices with a single Jordan...
Estimating directions of arrival (DOA) without knowledge of the source number is regarded as a challenging task, particularly when coherence among sources exists. Researchers have trained deep learning (DL)-based models to attack the problem of DOA e...
In this study, a fractional nonlinear mixed integro-differential equation (Fr-NMIDE) is presented and has a general discontinuous kernel based on position and time space. Conditions of the existence and uniqueness of the solution is provided through...
Regional-scale gravity imaging is limited by the size of the sensitivity matrix: a direct three-dimensional formulation of the gravity operator requires on the order of
Noise suppression capacity in multiple-input multiple-output (MIMO) sonar signal processing is derived under the assumption of white Gaussian noise. However, underwater noise mainly includes white Gaussian noise and colored noise. There exists a cert...
In this paper, the authors consider a problem with comprehensive properties in terms of form and content in the space
In this study, we investigate a class of mixed fractional partial integro-differential equations (FrPI-DE) involving symmetric singular kernels. The considered model problem involves Caputo fractional derivatives and integral operators that describe...
This work studies an integro-fractional differential equation (I-FrDE) with a generalized symmetric singular kernel. The scientific approach in this study was to transform the integro-differential equation (I-DE) into a mixed integral equation (MIE)...
In this study we have given some upper bounds for the spectral and lp norms of Cauchy-Toeplitz and Cauchy-Hankel matrices of the forms T = [1/(1/2 + |i + j|]n×n and H= [1/(1/2 + (i + j))]n×n respectively.
Modern investigation techniques (e.g., metabolomic, proteomic, lipidomic, genomic, transcriptomic, phenotypic), allow to collect high-dimensional data, where the number of observations is smaller than the number of features. In such cases, for statis...
This paper focuses on reducing the computational cost of a GNC Algorithm for deblurring images when dealing with full symmetric Toeplitz block matrices composed of Toeplitz blocks. Such a case is widespread in real cases when the PSF has a vast range...
For 5G and beyond cellular communication systems, new coding and modulation techniques are suggested to reach the requirements of high data rate and quality of service. In this paper, a new space-time coded orthogonal transform division multiplexing...
The direction-of-arrivals (DOA) estimation with an unfolded coprime linear array (UCLA) has been investigated because of its large aperture and full degrees of freedom (DOFs). The existing method suffers from low resolution and high computational com...
We reveal the analytic relations between a matrix permanent and major nature’s complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathe...
In this paper, the two-dimensional DOA estimation problem of coherent signals in an electromagnetic vector sensor (EMVS) array is studied. A new decorrelation method is proposed by extending the multiple-Toeplitz matrices reconstruction (MTOEP) metho...
In this study, we have established the bounds for the \(\ell_p \) norms and the Euclidean norm of almost GCD Cauchy-Toeplitz, almost GCD Cauchy-Hankel and GCD matrices, respectively.
This paper shows that using the Padé–Laplace (PL) method for deconvolution of multi-exponential functions (stress relaxation of polymers) can produce ill-conditioned systems of equations. Analysis of different sets of generated data points from known...
This study focuses on a class of perturbed Dirichlet–Neumann tridiagonal (PDNT) Toeplitz matrices, mainly exploring their eigenvalue sensitivity and inverse problems. By the explicit expressions for eigenvalues and eigenvectors of PDNT Toeplitz...
This paper proposes a fast epileptic seizure detection method to allow for early clinical intervention. The primary goal is to enhance computational and predictive performance to make the method viable for online implementation. An advanced Line Spec...
Let A be an
In this paper, a novel direction of arrival (DOA) estimation algorithm called the Toeplitz fourth order cumulants multiple signal classification method (TFOC-MUSIC) algorithm is proposed through combining a fast MUSIC-like algorithm termed the modifi...
In a distributed frequency-modulated continuous waveform (FMCW) radar system, the echo data collected are not continuous in the azimuth direction, so the imaging effect of the traditional range-Doppler (RD) algorithm is poor. Sparse Bayesian learning...
We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toe...
In this paper, an off-grid direction-of-arrival (DoA) estimation algorithm which can work on a non-uniform linear array (NULA) is proposed. The original semidefinite programming (SDP) representation of the atomic norm exploits a summation of one-rank...
Tempered fractional diffusion equations constitute a critical class of partial differential equations with broad applications across multiple physical domains. In this paper, the Crank–Nicolson method and the tempered weighted and shifted Gr&uu...
A trivially zero minor of a matrix is a minor having all its terms in the Leibniz formula equal to zero. A matrix is superregular if all of its minors that are not trivially zero are nonzero. In the area of Coding Theory, superregular matrices over f...
The accurate analysis of periodic surface acoustic wave (SAW) structures by combined finite element method and boundary element method (FEM/BEM) is important for SAW design, especially in the extraction of couple-of-mode (COM) parameters. However, th...
Under the background of spatially correlated color noise, the incidence angle of a jamming signal in a high-speed moving platform rapidly changes, which leads to the degradation of the anti-interference performance and the waveform distortion of the...
Given a real symmetric matrix, several inclusion and exclusion intervals containing its eigenvalues can be given. In this paper, for symmetric positive Toeplitz matrices, we provide an inclusion interval and, under an additional hypothesis, we also g...
With a focus on the multivariable coupling characteristics in a cross-directional (CD) basis weight control system, we study the coupling characteristics of a CD control system and decoupling control, and we propose a novel multivariable interpolatio...
This paper proposes a new class of efficient preconditioners for variable-coefficient time–space fractional diffusion equations. The Caputo time-fractional derivative is discretized by the
For the discretized linear systems of the spatial fractional diffusion equations, we construct a class of a modified DTS iteration method and give its asymptotic convergence conditions. Then, we design a fast modified DTS preconditioner by replacing...
Estimates bounds for Carathéodory functions in the complex domain are applied to demonstrate sharp limits for the inverse of analytic functions. Determining these values is considered a more difficult task compared to finding the values of ana...
We are interested in fast and stable iterative regularization methods for image deblurring problems with space invariant blur. The associated coefficient matrix has a Block Toeplitz Toeplitz Blocks (BTTB) like structure plus a small rank correction d...
Computational cost tremendously restricts the wide application of conventional integral equation (IE) method in large-scale magnetotelluric (MT) modeling. A couple of obstacles limit the developments of traditional MT modeling based on the IE method....
This study deals with the problem of covariance matrix estimation for radar sensor signal detection applications with insufficient secondary data in non-Gaussian clutter. According to the Euclidean mean, the authors combined an available prior covari...
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