1,327 Results Found

This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bi...

In this work, we consider the heat transfer problems with phase change. The mathematical model is described through a two-phase Stefan problem and defined in the whole domain that contains frozen and thawed subdomains. For the numerical solution of t...

We address the challenge of efficiently approximating piecewise smooth functions, particularly those with jump discontinuities. Given function values on a uniform grid over a domain $\Omega$ in ${\mathbb{R}}^d$, we present a novel B-spline-based approximation frame...

In the Compressed Sensing (CS) framework, the underdetermined system of linear equation (USLE) can have infinitely many possible solutions. However, we intend to find the sparsest possible solution, which is $l_0$-norm minimization. However, finding an...

Here we study the quantitative multivariate approximation of perturbed hyperbolic tangent-activated singular integral operators to the unit operator. The engaged neural network activation function is both parametrized and deformed, and the related ke...

In this article, we introduce, for the first time, multivariate symmetrized and perturbed hyperbolic tangent-activated convolution-type operators in three forms. We present their approximation properties, that is, their quantitative convergence to th...

In this article, for the first time, the univariate symmetrized and perturbed hyperbolic tangent activated convolution-type operators of three kinds are introduced. Their approximation properties are presented, i.e., the quantitative convergence to t...

This paper presents a novel deep-learning network designed to detect intervals of jump discontinuities in single-variable piecewise smooth functions from their noisy samples. Enhancing the accuracy of jump discontinuity estimations can be used to fin...

In some applications, one is interested in reconstructing a function f from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we suggest a me...

Total variation (TV) is widely used in many image processing problems including the regularization of optical flow estimation. In order to deal with non differentiability of the TV regularization term, smooth approximations have been considered in th...

A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined with Fourier–Bessel series and Fourier–Bessel tran...

Approximation and some other basic properties of various linear and nonlinear operators are potentially useful in many different areas of researches in the mathematical, physical, and engineering sciences. Motivated essentially by this aspect of appr...

The isomorphism of Karoubi-Villamayor K-groups with smooth K-groups for monoid algebras over quasi stable locally convex algebras is established. We prove that the Quillen K-groups are isomorphic to smooth K-groups for monoid algebras over quasi-stab...

We study a Durrmeyer–Beta-type positive linear operator on the half-line, constructed from rising-factorial weights and a normalized beta-prime kernel. Exact raw moments through degree four and the corresponding central moments are derived unde...

We show that the viscosity approximation method coupled with the Krasnoselskii–Mann iteration generates a sequence that strongly converges to a fixed point of a given nonexpansive mapping in the setting of uniformly smooth Banach spaces. Our re...

In this article we present the $L_p$, $p\ge 1$, approximation properties of activated singular integral operators over the real line. We establish their approximation to the unit operator with rates. The kernels here come from neural network activation fu...

Penalty function methods are fundamental for solving constrained optimization problems, yet the widely used $l_1$ exact penalty function is non-differentiable and therefore incompatible with gradient-based algorithms. This paper proposes a continuously...

Sparse ergodic control provides a natural framework for long-run stochastic decision-making under resource constraints. Existing formulations, however, are typically restricted to control-affine systems with control-independent diffusion. When the di...

This paper addresses fundamental challenges in numerical approximation methods, focusing on balancing accuracy with shape-preserving properties. We present novel approaches that combine traditional spline methods with modern numerical techniques, ext...

In this paper, we provide a novel extended mixed differential model that is appealing to users because of its numerous free parameters. The motivation of this research arises from the opportunity for a general investigation of some outstanding classi...

We first study the error performances of the Vector Weak Rescaled Pure Greedy Algorithm for simultaneous approximation with respect to a dictionary $\mathcal{D}$ in a Hilbert space. We show that the convergence rate of the Vector Weak Rescaled Pure Greedy Algori...

In this paper, we study the approximation of continuous functions on a subclass of singular space—the subcartesian space. As is well known, the orbit space of the proper action of a Lie group on a smooth manifold is a subcartesian space. We pro...

Taylor–Young and Maclaurin series are widely used for approximating smooth functions around a given point. This study investigates a unified stochastic framework for Taylor-type expansions of functions by means of independent random variables....

In the context of increasing demand for secure and efficient communication networks, addressing the issue of mutual authentication in ethernet passive optical networks (EPONs) has become both valuable and practically significant. This paper proposes...

In this article, we employ the uniform and $L_p$, $1\le p<\infty$ approximation properties of general smooth multivariate singular integral operators over ${\mathbb{R}}^N$, $N\ge 1$. It is a trigonometric relief approach with detailed applications to the correspondin...

There has been a growing interest in expressivity of deep neural networks. However, most of the existing work about this topic focuses only on the specific activation function such as ReLU or sigmoid. In this paper, we investigate the approximation a...

The aim of this paper is to present and study nonlinear bivariate $C^1$ quadratic spline quasi-interpolants on uniform criss-cross triangulations for the approximation of piecewise smooth functions. Indeed, by using classical spline quasi-interpolants,...

In this article, we study the multivariate quantitative smooth approximation under differentiation of functions. The approximators here are multivariate neural network operators activated by the symmetrized and perturbed hyperbolic tangent activation...

In this work, we study the univariate quantitative smooth approximations, including both real and complex and ordinary and fractional approximations, under different functions. The approximators presented here are neural network operators activated b...

We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation...

This research focuses on the approximation properties of Kantorovich-type operators using Frobenius–Euler–Simsek polynomials. The test functions and central moments are calculated as part of this study. Additionally, uniform convergence a...

This manuscript associates with a study of Frobenius–Euler–Simsek-type Polynomials. In this research work, we construct a new sequence of Szász–Beta type operators via Frobenius–Euler–Simsek-type Polynomials to di...

In this paper, we solve a system of mixed variational inclusions involving a generalized Cayley operator and the generalized Yosida approximation operator. An iterative algorithm is suggested to discuss the convergence analysis. We have shown that ou...

This study presents a numerical and analytical investigation of the nonlinear smooth-discontinuous (SD) oscillator. The nonlinear restoring force is approximated by a fifth-order polynomial using a Taylor series expansion to simplify the governing eq...

In this paper, a novel class of quantum fractal functions is introduced based on the Meyer-König-Zeller operator $M_{q,n}$. These quantum Meyer-König-Zeller (MKZ) fractal functions employ $M_{q,n}f$ as the base function in the iterated function syste...

This article presents a new method for the extraction and measurement of the polyurethane layer of Cordura textile composites using optical coherence tomography. The knowledge of coating layer properties in these composites is very important, as it a...

In this work, we first establish a new connection between adjoint Bernoulli’s polynomials and gamma function as a new sequence of linear positive operators denoted by ${\mathfrak{S}}_{r,\varsigma ,\lambda }(.;.)$. Further, convergence results for these sequences o...

Gaussian filtering, being a convolution with a Gaussian kernel, is a widespread technique in image analysis and computer vision applications. It is the traditional approach for noise reduction. In some cases, performing the exact convolution can be c...

This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various funct...

In recent years, the tensor completion algorithm has played a vital part in the reconstruction of missing elements within high-dimensional remote sensing image data. Due to the difficulty of tensor rank computation, scholars have proposed many substi...

Sparse-signal recovery in noisy conditions is a problem that can be solved with current compressive-sensing (CS) technology. Although current algorithms based on $L_1$ regularization can solve this problem, the $L_1$ regularization mechan...

In this study, a smoothing method was applied to improve the accuracy of peak wave period estimation using water surface elevation data collected from two oceanographic and meteorological observation towers situated on the western coast of the Korean...

Bootstrap methods are used for bandwidth selection in: (1) nonparametric kernel density estimation with dependent data (smoothed stationary bootstrap and smoothed moving blocks bootstrap), and (2) nonparametric kernel hazard rate estimation (smoothed...

Meta-model sre generally applied to approximate multi-objective optimization, reliability analysis, reliability based design optimization, etc., not only in order to improve the efficiencies of numerical calculation and convergence, but also to facil...

We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter $\lambda \in [-1,1]$ and calculate their moments. The uniform convergence of the operator and global approximation result by means of...

In the present article, we introduce the bivariate variant of Beta integral type operators based on Appell polynomials via q-calculus. We study the local and global type approximation properties for these new operators. Next, we introduce the GBS for...

This work proposes a resampling technique to approximate the smoothing parameter of Beran’s estimator. It is based on resampling by the smoothed bootstrap and minimising the bootstrap approximation of the mean integrated squared error to find the boo...

The spatial-based method has become the most widely used method in improving the visibility of images. The visibility improving is mainly to remove the noise in the image, in order to trade off denoising and detail maintaining. A novel adaptive non-l...

Recent studies suggest that the minimum error entropy (MEE) criterion can outperform the traditional mean square error criterion in supervised machine learning, especially in nonlinear and non-Gaussian situations. In practice, however, one has to est...

A numerical simulation method combining the detailed chemical reaction mechanism of methane deflagration with an approximate real tunnel structure was proposed to confirm whether the unevenness of the tunnel wall during a coal mine gas explosion can...