The hardware of the matrix inversion architecture using QR decomposition with Givens Rotations (GR) and a back substitution (BS) block is required for many signal processing algorithms. However, the hardware of the GR algorithm requires the implement...
This paper studies new characterizations and expressions of the weak group (WG) inverse and its dual over the quaternion skew field. We introduce a dual to the weak group inverse for the first time in the literature and give some new characterization...
Numerical inverse Z-transformation (NIZT) methods have been efficiently used in engineering practice for a long time. In this paper, we compare the abilities of the most widely used NIZT methods, and propose a new variant of a classic NIZT method bas...
In order to solve the problem that the measurement noise covariance may be unknown or change with time in actual multi-target tracking, this paper brings the variational Bayesian approximation method into the trajectory probability hypothesis density...
In geophysical inversion issues, the Jacobian matrix computation takes the greatest time, and it is the most significant factor limiting the inversion’s calculation speed. We think that the correctness of the inverse problem is determined by th...
Some iterative schemes with memory were designed for approximating the inverse of a nonsingular square complex matrix and the Moore–Penrose inverse of a singular square matrix or an arbitrary
Progressive iterative approximation (PIA) technique is an efficient and intuitive method for data fitting. In CAGD modeling, if the given data points are taken as initial control points, PIA process generates a series of shaping curves by adjusting t...
This Special Issue contains 14 articles from the MDPI journal Symmetry on the general subject area of “Special Functions and Polynomials”, written by scholars belonging to different countries of the world. A similar number of submitted ar...
A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A. For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the matrix is singular, an approximat...
This paper is devoted to the approximation of matrix pth roots. We present and analyze a family of algorithms free of inverses. The method is a combination of two families of iterative methods. The first one gives an approximation of the matrix inver...
The concept presented in this paper is based on previous dynamical methods to realize a time-varying matrix inversion. It is essentially a set of coupled ordinary differential equations (ODEs) which does indeed constitute a recurrent neural network (...
In penetrating radar waveform inversion, the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm only needs to store the most recent gradients and model parameters to approximate the Hessian matrix, which effectively...
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Padé approximation, sometimes accompanied by the Schur decomposition. In this work, we present a Taylor serie...
The problem of inverse kinematics is essential to consider while dealing with the robot’s mechanical structure in almost all applications. Since the solution of the inverse kinematics problem is very complex, many research efforts have been working t...
Massive multiple-input multiple-output (M-MIMO) is a substantial pillar in fifth generation (5G) mobile communication systems. Although the maximum likelihood (ML) detector attains the optimum performance, it has an exponential complexity. Linear det...
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...
The kinematic control of manipulators has extensive applications in modern industry. Precise control enables robotic manipulators to perform diverse complex tasks, boost production efficiency/quality, and cut labor costs and safety risks. Kinematic c...
Inverse problems have numerous important applications in science, engineering, medicine, and other disciplines. In this study, we present a numerical solution for a one-dimensional parabolic inverse problem with energy overspecification at a fixed sp...
Three-dimensional inversion of airborne transient electromagnetic (ATEM) data is computationally demanding because it requires repeated forward simulations and sensitivity calculations. Previous Krylov-subspace studies have substantially improved the...
The paper considers one of the possible statements of inverse problems in gravimetric and magnetometric remote sensing, proposes a new approach to its solution and formulates algorithms that implement this approach. The problem under consideration co...
In atmospheric science we are confronted with inverse problems arising in applications associated with retrievals of geophysical parameters. A nonlinear mapping from geophysical quantities (e.g., atmospheric properties) to spectral measurements can b...
The invariant imbedding T-matrix (IIM T-matrix) model is regarded as one of the most promising models for calculating the scattering parameters of non-spherical particles. However, the IIM T-matrix model needs to be iterated along the radial directio...
On resource-constrained edge hardware, fixed-point Transformer inference is constrained by GEMM kernels and non-GEMM normalization paths. In LayerNorm and Softmax, division, inverse square root, and denominator reciprocal operations complicate fixed-...
The matrix logarithm function has applicability in many engineering and science fields. Improvements in its calculation, from the point of view of both accuracy and/or execution time, have a direct impact on these disciplines. This paper describes a...
This research investigates the use of charge coupled device (abbreviated as CCD) linear image sensors in an optical tomographic instrumentation system used for sizing particles. The measurement system, consisting of four CCD linear image sensors are...
We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the...
A new version of the linear integral representation method is developed for solving inverse problems in geophysics. This approach is applied to the interpretation of anomalous time-dependent field data. The reconstruction of field elements is reduced...
The accuracy of microseismic moment tensor inversion critically depends on the spatial configuration of surface sensor arrays, quantified by the condition number
This paper proposes an inverse model for raindrop size distribution (DSD) retrieval with polarimetric radar variables. In this method, a forward operator is first developed based on the simulations of monodisperse raindrops using a T-matrix method, a...
3D magnetotelluric (MT) inversion based on the Gauss–Newton (GN) framework plays an important role in deep mineral exploration by imaging subsurface electrical conductivity structures. However, large-scale 3D MT inversion remains computationall...
Gravity inversion plays a crucial role in mineral exploration and resource evaluation, yet conventional depth-weighting methods often impose uniform resolution across all depths and fail to effectively delineate anomaly boundaries. This study present...
In order to reduce the computational complexity of the inverse matrix in the regularized zero-forcing (RZF) precoding algorithm, this paper expands and approximates the inverse matrix based on the truncated Kapteyn series expansion and the correspond...
In the application of a micro-/nano-mechanical resonator, the position of an accreted particle and the resonant frequencies are measured by two different physical systems. Detecting the particle position sometimes can be extremely difficult or even i...
To solve the problem of unknown state noises and uncertain measurement noises inherent in underwater cooperative navigation, a new Variational Bayesian (VB)-based Adaptive Extended Kalman Filter (VBAEKF) for master–slave Autonomous Underwater V...
In massive multiple-input multiple-output (M-MIMO) systems, a detector based on maximum likelihood (ML) algorithm attains optimum performance, but it exhaustively searches all possible solutions, hence, it has a very high complexity and realization i...
The Luk-Ulo Melange Complex (LMC) is characterized by a chaotic assemblage of mixed rocks with a block-in-matrix fabric. The exposed blocks consist of various scattered rock types, trending in an ENE-WSW direction. In the case of Mt. Parang, the orig...
This paper investigates the inverse problem of identifying a time-dependent source term in multi-term time–space fractional diffusion Equations (TSFDE). First, we rigorously establish the existence and uniqueness of strong solutions for the ass...
Seismic velocities are related to the solid matrices and the pore fluids. The bulk and shear moduli of dry rock are the primary parameters to characterize solid matrices. Amplitude variation with offset (AVO) or amplitude variation with incidence ang...
All elements of the scattering matrix have been numerically studied for particles of irregular shapes whose size is much larger than incident wavelength. The calculations are performed in the physical optics approximation for a particle size of 20 &m...
For multi-user uplink massive multiple input multiple output (MIMO) systems, minimum mean square error (MMSE) criterion-based linear signal detection algorithm achieves nearly optimal performance, on condition that the number of antennas at the base...
Stochastic processes are useful and important for modeling the evolution of processes that take different states over time, a situation frequently found in fields such as medical research and engineering. In a previous paper and within this framework...
In the presented study, multi-parameter inversion in the presence of attenuation is used for the reconstruction of the P- and the S- wave velocities and the density models of a synthetic shallow subsurface structure that contains a dipping high-veloc...
Signal detection is a serious challenge for uplink massive multiple-input multiple-output (MIMO) systems. The traditional linear minimum-mean-squared error (MMSE) achieves good detection performance for such systems, but involves matrix inversion, wh...
This paper investigates statistical methods for estimating unknown lifetime parameters using a progressive first-failure censoring dataset. The failure mode’s lifetime distribution is modeled by the odd-generalized-exponential–inverse-Wei...
This paper presents a computationally efficient soft detection scheme for massive multiple-input multiple-output (MIMO) systems. The proposed scheme adopts joint iterative detection and decoding (JIDD) methods for their capacity limiting performances...
We focus on inverse preconditioners based on minimizing
We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup...
In the paper, orthogonal transforms based on proposed symmetric, orthogonal matrices are created. These transforms can be considered as generalized Walsh–Hadamard Transforms. The simplicity of calculating the forward and inverse transforms is one of...
The Kriging surrogate model in complex simulation problems uses as few expensive objectives as possible to establish a global or local approximate interpolation. However, due to the inversion of the covariance correlation matrix and the solving of Kr...
New observations of ocean surface topography obtained by wide-swath satellite interferometry require new capabilities to process spatially correlated errors in order to assimilate these data into numerical models. The sea surface height (SSH) variati...
of 4