Results 31 to 40 of about 532 (83)

Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

, 2007
The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a natural function
F.J. Narcowich, G.J.O. Jameson, J. Levesley, J. Yoon, J. Yoon, R. A. Brownlee, R. Brownlee, W.A. Light, W.A. Light   +8 more
core   +1 more source

Efficient α-Dense Curve Strategies for Multiple Integrals over Hyper-rectangle Regions

Annals of the West University of Timisoara: Mathematics and Computer Science
In this paper, we propose an approximation technique to compute multiple integrals of a non-negative real continuous function over a hyper-rectangle Ω of ℝn.
Rahal Mohamed, Guettal Djaouida
doaj   +1 more source

Quantitative estimates for perturbed sampling Kantorovich operators in Orlicz spaces

Demonstratio Mathematica
In the present work, we establish a quantitative estimate for the perturbed sampling Kantorovich operators in Orlicz spaces, in terms of the modulus of smoothness, defined by means of its modular functional.
Costarelli Danilo, De Angelis Eleonora, Vinti Gianluca   +2 more
doaj   +1 more source

A note on an integral associated with the Kelvin ship-wave pattern [PDF]

, 2015
The velocity potential in the Kelvin ship-wave source can be partly expressed in terms of space derivatives of the single integral F(x, ρ, α) = ʃ ∞ −∞ exp [−1/2ρ cosh(2u − iα)] cos(x cosh u) du, where (x, ρ, α) are cylindrical polar coordinates with ...
Paris, R. B.
core   +2 more sources

Gradient bounds for Wachspress coordinates on polytopes

, 2013
We derive upper and lower bounds on the gradients of Wachspress coordinates defined over any simple convex d-dimensional polytope P. The bounds are in terms of a single geometric quantity h_*, which denotes the minimum distance between a vertex of P and ...
Floater, Michael, Gillette, Andrew, Sukumar, N.   +2 more
core   +1 more source

Unique compact representation of magnetic fields using truncated solid harmonic expansions

European Journal of Applied Mathematics
Precise knowledge of magnetic fields is crucial in many medical imaging applications such as magnetic resonance imaging (MRI) or magnetic particle imaging (MPI), as they form the foundation of these imaging systems. Mathematical methods are essential for
Marija Boberg, Tobias Knopp, Martin Möddel   +2 more
doaj   +1 more source

Towards a More General Type of Univariate Constrained Interpolation With Fractal Splines

, 2015
Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional nonrecursive rational ...
Chand, A. K. B., Reddy, K. M., Viswanathan, P.   +2 more
core   +1 more source

The mathematics of adversarial attacks in AI – why deep learning is unstable despite the existence of stable neural networks

European Journal of Applied Mathematics
The unprecedented success of deep learning (DL) makes it unchallenged when it comes to classification problems. However, it is well established that the current DL methodology produces universally unstable neural networks (NNs).
Alexander Bastounis, Anders Hansen, Verner Vlačić   +2 more
doaj   +1 more source

Compactly supported radial basis functions: how and why? [PDF]

, 2012
The use of radial basis functions have attracted increasing attention in recent years as an elegant scheme for high-dimensional scattered data approximation, an accepted method for machine learning, one of the foundations of mesh-free methods, an ...
Zhu, S.
core   +3 more sources

Richards's curve induced Banach space valued multivariate neural network approximation. [PDF]

Arab J Math, 2023
Anastassiou GA, Karateke S.
europepmc   +1 more source