Results 11 to 20 of about 2,239 (225)

Global smoothness preservation by singular integrals [PDF]

Proyecciones (Antofagasta), 2018
Here is established that the well-known singular integrals of Picard, Poisson-Cauchy and Gauss- Weierstrass fulfill the "global smoothness preservation" property. J. e., they "ripple" less than the function they are applied on, that is producing a nice approximation to the unit. The associated inequalities are sharp.
Anastassiou, George A.
core   +5 more sources

Global smoothness and approximation by generalized discrete singular operators [PDF]

Journal of Numerical Analysis and Approximation Theory, 2014
In this article we continue with the study of generalized discrete singular operators over the real line regarding their simultaneous global smoothness preservation property with respect to \(L_{p}\) norm for \( 1\leq p\leq \infty ,\) by involving ...
George A. Anastassiou, Merve Kester
doaj   +4 more sources

Best constants in preservation of global smoothness for Szász–Mirakyan operators [PDF]

Journal of Mathematical Analysis and Applications, 2008
For \(t>0\), the Szász-Mirakyan operator \(S_{t}\) is defined by \[ S_{t}f(x):=e^{-xt}\,\sum_{k=0}^{\infty}f\Big(\frac{k}{t}\Big)\frac{(tx)^{k}}{k!}, \quad x\geq 0, \] where \(f\) is any real function defined on \([0,\,\infty)\) such that \(S_{t}| f| (x)0, \quad C_{t}:=\sup_{\delta>0}C_{t}(\delta), \] where \[ w(f;\delta):=\sup\big\{| f(x)-f(y)| \,:x,y\
Adell, José A., Lekuona, Alberto
openaire   +3 more sources

Approximation by Symmetrized and Perturbed Hyperbolic Tangent Activated Convolution-Type Operators [PDF]

Mathematics
In this article, for the first time, the univariate symmetrized and perturbed hyperbolic tangent activated convolution-type operators of three kinds are introduced.
George A. Anastassiou
doaj   +2 more sources

Multivariate Perturbed Hyperbolic Tangent-Activated Singular Integral Approximation [PDF]

Mathematics
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 kernel
George A. Anastassiou
doaj   +2 more sources

Best Constants in Global Smoothness Preservation Inequalities for Some Multivariate Operators [PDF]

Journal of Approximation Theory, 1999
Using a probabilistic representation of positive operators going back to the classical paper of S. Bernstein the authors give sharp estimates for the modulus of continuity of \(L_tf\). Here \(\{L_t\xi_{t\in T}\) is an approximating family of positive operators acting in the space \(\{f:I^k\to\mathbb{R}\); \(\sup_{x,y}| f(x)-f(y)|
de la Cal, Jesús, Valle, Ana M.
openaire   +3 more sources

The second order modulus revisited: remarks, applications, problems [PDF]

Journal of Numerical Analysis and Approximation Theory
Several questions concerning the second order modulus of smoothness are addressed in this note. The central part is a refined analysis of a construction of certain smooth functions by Zhuk and its application to several problems in approximation theory,
Heiner Gonska, Ralitza K. Kovacheva
doaj   +3 more sources

General theory of global smoothness and approximation by smooth singular operators [PDF]

, 2011
In this article we continue with the study of smooth general singular integral operators over the real line regarding their simultaneous global smoothness preservation property with respect to the Lp norm, 1≤p≤∞, by involving higher order moduli of ...
Razvan A. Mezei, Anastassiou, George A., Mezei, Razvan A., George A. Anastassiou   +3 more
core   +1 more source

Global smoothness and uniform convergence of smooth Poisson-Cauchy type singular operators [PDF]

, 2009
In this article we introduce the smooth Poisson-Cauchy type singular integral operators over the real line. Here we study their simultaneous global smoothness preservation property with respect to the Lp norm, 1 ≤ p ≤ ∞, by involving higher order moduli ...
Anastassiou, George A., Mezei, Razvan A.
core   +1 more source

LiDAR-Guided Illumination-Aware 3D Gaussian Splatting for Cultural Heritage [PDF]

ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences
To address the issues of geometric distortion and loss of details in 3D modeling for complex cultural heritage scenes, this paper proposes an improved 3D Gaussian Splatting (3DGS) reconstruction method that integrates LiDAR and illumination-awareness ...
X. Liu, X. Li, W. Li, T. Liu, W. Sun, S. Zhang   +5 more
doaj   +1 more source