14 papers · ranked by Valyu relevance
Jieun Song, Bumjoo Lee, Zhengguo Li
In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares. In time-sensitive applications or in embedded systems with limited resources, the runtime of the approximate function is as crucial as its…
Nives Brajčić Kurbaša, Blaž Gotovac, Vedrana Kozulić, Hrvoje Gotovac + 1 more
'Philip Broadbridge'] Estimation of the probability density function from the statistical power moments presents a challenging nonlinear numerical problem posed by unbalanced nonlinearities, numerical instability and a lack of convergence, especially for larger numbers of moments. Despite many numerical improvements…
Francisco Martínez, Mohammed K. A. Kaabar
A newly proposed generalized formulation of the fractional derivative, known as Abu-Shady-Kaabar fractional derivative, is investigated for solving fractional differential equations in a simple way. Novel results on this generalized definition is proposed and verified, which complete the theory introduced so far. In…
George A. Anastassiou, Seda Karateke
Here, we present multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ${\mathbb{R}}^{N},$ $N\in{\mathbb{N}},$ by the multivariate normalized, quasi-interpolation, Kantorovich-type and quadrature-type neural network operators. We examine also the case of…
Atallah El-Shenawy, Mohamed El-Gamel, Mostafa Abouelsaid
This work introduces an innovative nonlinear model of hepatitis B virus (HBV) dynamics, emphasizing the utilization of the Dickson collocation method for numerical simulation. Our method, in contrast to conventional techniques, adeptly tackles the complex interactions between the virus and the host’s immune response…
Alexandre Wagemakers, Vipul Periwal
We explore a family of numerical methods, based on the Steffensen divided difference iterative algorithm, that do not evaluate the derivative of the objective functions. The family of methods achieves second-order convergence with two function evaluations per iteration with marginal additional computational cost. An…
Arieh Iserles, Georg Maierhofer
The efficient approximation of highly oscillatory integrals plays an important role in a wide range of applications. Whilst traditional quadrature becomes prohibitively expensive in the high-frequency regime, Levin methods provide a way to approximate these integrals in many settings at uniform cost. In this work, we…
Md. Humayun Kabir, Md. Shafiqul Islam, Md. Kamrujjaman
Title: Graphical abstract
Lewis Marsh, David Beers
The Euler characteristic transform (ECT) is a signature from topological data analysis (TDA) which summarises shapes embedded in Euclidean space. Compared with other TDA methods, the ECT is fast to compute and it is injective on a broad class of shapes. However, small perturbations of a shape can lead to large…
Jing Guo, Xianjun Zhu, Wenfeng Li, Hui Li + 1 more
As an essential part of classical analysis, Ostrowski and Čebyšev type inequalities have recently attracted considerable attention. Due to its universality, the non-additive integral inequality takes several forms, including Sugeno integrals, Choquet integrals, and pseudo-integrals. Set-valued analysis, a well-known…
Anthony LoPrete, Johannes Burge
The full width at half maximum (FWHM) is a useful quantity for characterizing the bandwidth of unimodal functions. However, a closed-form expression for the FWHM of gamma-shaped functions - i.e. functions that are shaped like the gamma distribution probability density function (PDF) - is not widely available. Here, we…
Dai-Nghia Vy, Van-Thuan Nguyen, Quyet-Thang Huynh, Trung-Nghia Phung + 2 more
Context: Many models based on S-shaped functions demonstrate their advantages in non-homogeneous Poisson process software reliability modeling. However, three well-known types have been used without deep mathematical evaluation. Furthermore, some other promising S-shaped functions should be aimed at. Objectives: (1)…
Mohammad Faisal Khan, Mohammed Abaoud, Naeem Ahmad, Muqrin A. Almuqrin + 1 more
'Muqrin A. Almuqrin' 'Mohamed Kamel Riahi'] Function theory research has long struggled with the challenge of deriving sharp estimates for the coefficients of analytic and univalent functions. Researchers have advanced the field by developing and applying a variety of approaches to get these bounds. In the current…
Ibtehal Alazman, Rabha W. Ibrahim
Numerous special functions, including the beta function, hypergeometric functions, and other orthogonal polynomials, are closely connected to the gamma function. Recently, gamma function has been enhanced by adding a new parameter. As a consequence, this gamma is called the parametric gamma function or b-gamma…