1,102 Results Found

This study proposes a decoupling approach based on first-order exponential function approximation for reliability-based optimization. It establishes an explicit relationship between the failure probability and design parameters within only one implem...

In this paper, we study the weighted approximation properties of a family of Szász–Mirakyan-type operators preserving two exponential functions on the unbounded interval $[0,\infty )$. The operators act on exponential weighted spaces and a...

A significant reduction in the time required to obtain an estimate of the mean frequency of the spectrum of Doppler signals when seeking to measure the instantaneous velocity of dangerous near-Earth cosmic objects (NEO) is an important task being dev...

Error estimates of pointwise approximation, that are not possible by polynomials, are obtained by simple rational operators based on exponential-type meshes, improving previous results. Rational curves deduced from such operators are analyzed by Disc...

We examine a Szász–Mirakyan–Durrmeyer type operator that reproduces the functions 1 and $e^{2ax}$ for a fixed parameter $a>0.$ While its exponential reproduction property has been described in the classical literature, the effect of ex...

Variational Bayesian Approximation (VBA) is a fast technique for approximating Bayesian computation. The main idea is to assess the joint posterior distribution of all the unknown variables with a simple expression. Mean–Field Variational Bayes...

A new way to compute the Taylor polynomial of a matrix exponential is presented which reduces the number of matrix multiplications in comparison with the de-facto standard Paterson-Stockmeyer method for polynomial evaluation. Combined with the scalin...

Surface modeling is closely related to interpolation and approximation by using level set methods, radial basis functions methods, and moving least squares methods. Although radial basis functions with global support have a very good approximation ef...

The high numerical computing cost of time-fractional diffusion equation (tFDE) models over long time periods is a major obstacle to their real-world applications. Therefore, this study presents a rapid adaptive finite difference method, which uses th...

We study $L_2$-approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters ${\gamma }_j$ and ${\alpha }_j$ for $j\in \mathbb{N}$. W...

This paper introduces a Gegenbauer-based fractional approximation (GBFA) method for high-precision approximation of the left Riemann–Liouville fractional integral (RLFI). By using precomputable fractional-order shifted Gegenbauer integration ma...

Using the generalized stationary renewal distribution (also called the equilibrium transform) for arbitrary distributions with a finite non-zero first moment, we prove moment-type error-bounds in the Kantorovich distance for the exponential approxima...

There are a couple of purposes in this paper: to study a problem of approximation with exponential functions and to show its relevance for economic science. The solution of the first problem is as conclusive as it can be: working with the max-norm, w...

The exponentiated exponential distribution has received great attention from many statisticians due to its popularity, many applications, and the fact that it is an efficient alternative to many famous distributions such as Weibull and gamma distribu...

In this paper, function approximation is utilized to establish functional series approximations to integrals. The starting point is the definition of a dual Taylor series, which is a natural extension of a Taylor series, and spline based series appro...

We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for...

This paper introduces a new family of Szász–Mirakyan-type operators defined by a convex combination of two Poisson-type constructions. The operators preserve the constant function and provide a continuous transition between different exp...

Based on the traditional Black–Scholes option pricing model, we consider a European option pricing model with transaction costs and dividend payments. In our paper, we use the Galerkin method to study the existence of a solution of this model....

The exponential dispersion model (EDM) generated by the Landau distribution, denoted by EDM-EVF (exponential variance function), belongs to the Tweedie scale with power infinity. Its density function does not have an explicit form and, as of yet, has...

In this paper, we propose a novel, highly accurate numerical algorithm for matrix exponentials (MEs). The algorithm is based on approximating Putzer’s algorithm by analytically solving the ordinary differential equation (ODE)-based coefficients...

For the calculation of thermal processes of canned food, the original formula method of Ball is still widely used for its accuracy and safety. However, it requires the consultation of tables that Ball prepared and the relative interpolation of the da...

In this paper, we focus on the computation of Caputo-type fractional differential equations. A high-order predictor–corrector method is derived by applying the quadratic interpolation polynomial approximation for the integral function. In order...

Exponential integrator (EI) method based on Krylov subspace approximation is a promising method for large-scale transient circuit simulation. However, it suffers from the singularity problem and consumes large subspace dimensions for stiff circuits w...

From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain preci...

Using progressive first-failure censored samples, we mainly study the inferences of the unknown parameters and the reliability and failure functions of the Inverted Exponentiated Half-Logistic distribution. The progressive first-failure censoring is...

In this research, random censoring is employed as a methodology for parameter estimation within the context of an exponential distribution. These parameter estimations are conducted using both the Bayesian and maximum likelihood approaches. In the Ba...

Time–space fractional diffusion equations are widely used to model anomalous transport in heterogeneous biological tissues, where memory effects, spatial nonlocality, and coefficient variability are intrinsically coupled. However, existing nume...

This paper presents a fast Crank–Nicolson L1 finite difference scheme for the two-dimensional time fractional mobile/immobile diffusion equation with weakly singular solution at the initial moment. First, the time fractional derivative is discr...

In off-boundary computations of layer potentials, the near-singularities in integrals near the boundary presents challenges for conventional quadrature methods in achieving high precision. Additionally, the significant complexity of $\mathcal{O}\left(n^2\right)$ interaction...

Competing risks are frequently overlooked, and the event of interest is analyzed with conventional statistical techniques. In this article, we consider the analysis of bi-causes of failure in the context of competing risk models using the extension o...

In this article, the estimation of the parameters and the reliability and hazard functions for Weibull inverted exponential (WIE) distribution is considered based on progressive first-failure censoring (PFFC) data. For non-Bayesian inference, maximum...

Left-truncated and right-censored data are widely used in lifetime experiments, biomedicine, labor economics, and actuarial science. This article discusses how to resolve the problems of statistical inferences on the unknown parameters of the exponen...

Time-fractional diffusion equations (TFDEs) are essential for modeling anomalous transport in heterogeneous media, but high-fidelity long-time simulations face two bottlenecks: the $O\left(N^2\right)$ complexity of non-local fractional derivatives, and the spatial...

The article deals with the approximation of the results of experimental measurement of coating of the inner surface of slim pipes with special oil, using a dispersion oil fraction. The reason for such treatment of the inner surface of the tubes is th...

Wave equations with Caputo fractional damping produce power-law attenuation, but their non-local memory term is costly, and stability proofs for nonlinear variants involve long, error-prone algebra. We discretise a one-dimensional wave equation with...

In this article, a considerably efficient predictor-corrector method (PCM) for solving Atangana–Baleanu Caputo (ABC) fractional differential equations (FDEs) is introduced. First, we propose a conventional PCM whose computational speed scales w...

We develop a shared denominator Carathéodory–Fejér (CF) method for efficiently evaluating linear combinations of $\phi$-functions for matrices whose spectrum lies in the negative real axis, as required in exponential integrators fo...

This study proposes an L1 discretization scheme (an accurate second-order finite difference method) for time-fractional diffusion equations involving the Caputo-type Erdélyi–Kober operator, which models anomalous diffusion. Our key contr...

The Jeffreys divergence is a renown arithmetic symmetrization of the oriented Kullback–Leibler divergence broadly used in information sciences. Since the Jeffreys divergence between Gaussian mixture models is not available in closed-form, various tec...

The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrel...

The general framework for quantitative technical analysis of market prices is revisited and extended. The concept of a global time-translation invariance and its spontaneous violation and restoration is introduced and discussed. We find that differen...

The present study elaborates on the thermal distribution and efficiency of a longitudinal rectangular fin with exponentially varying temperature-dependent thermal conductivity and heat transfer coefficient concerning internal heat generation. Also, t...

In this study, two new integrated control charts, named $T^2$-MAE chart and MS-MAE chart, are introduced for monitoring the quality of a process when the mathematical form of nonlinear profile model for quality measure is complicated and unable to be sp...

The Hurwitz zeta-function $\zeta (s,\alpha )$, $s=\sigma +it$, with parameter $0<\alpha ⩽1$ is a generalization of the Riemann zeta-function $\zeta \left(s\right)$ ($\zeta (s,1)=\zeta \left(s\right)$) and was introduced at the end of the 19th century. The function $\zeta ($...

The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step has been rep...

In this paper, we construct a new variant of the classical Szász–Mirakyan operators, $M_n$, which fixes the functions 1 and $e^{ax},x\ge 0,a\in \mathbb{R}$. For these operators, we provide a quantitative Voronovskaya-type result. The uniform weighted convergence of $M_n$ and...

In this paper, we introduce $(p,q)$-cosine Euler polynomials. From these polynomials, we find several properties and identities. Moreover, we find the circle equations of approximate roots for $(p,q)$-cosine Euler polynomials by using a computer.

In recent years, the Poisson lognormal mixed model has been frequently used in modeling count data because it can accommodate both the over-dispersion of the data and the existence of within-subject correlation. Since the likelihood function of this...

The Euler difference approach has become a prevalent tool in the research of integral order differential equations. Nevertheless, a review of the literature reveals a dearth of studies examining fractional order models using the exponential Euler dif...

Stirling approximation of the factorials and multinominal coefficients are generalized based on the κ-generalized functions introduced by Kaniadakis. We have related the κ-generalized multinominal coefficients to the κ-entropy by introducing a new κ-...