Approximation properties of certain interpolation operators of entire exponential type inL p (−∞,+∞) spaces

1991 ◽  
Vol 7 (4) ◽  
pp. 289-308 ◽  
Author(s):  
Liu Youngping
Keyword(s):  
Exponential Type ◽  
Approximation Properties ◽  
Interpolation Operators

scholarly journals Semi-Exponential Operators

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 637
Author(s):  
Monika Herzog
Keyword(s):  
Exponential Type ◽  
Probabilistic Approach ◽  
Weighted Spaces ◽  
Approximation Properties

In this paper we study approximation properties of exponential-type operators for functions from exponential weighted spaces. We focus on some modifications of these operators and we derive a new example of such operators. A probabilistic approach for these modifications is also demonstrated.

scholarly journals Exponential moments and simultaneous approximation properties for Durrmeyer type operators with weights of Szasz basis functions

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1465-1475
Author(s):  
Antonio-Jesús López-Moreno ◽  
Vijay Gupta
Keyword(s):  
Exponential Type ◽  
Exponential Growth ◽  
Simultaneous Approximation ◽  
Basis Functions ◽  
Approximation Properties ◽  
Exponential Functions ◽  
Quantitative Estimates ◽  
Exponential Moments ◽  
Durrmeyer Type Operators ◽  
Derivatives Of

The present paper deals with the approximation properties for exponential functions of general Durrmeyer type operators having the weights of Sz?sz basis functions. Here we give explicit expressions for exponential type moments by means of which we establish, for the derivatives of the operators, the Voronovskaja formulas for functions of exponential growth and the corresponding weighted quantitative estimates for the remainder in simultaneous approximation.

scholarly journals Robust Numerical Upscaling of Elliptic Multiscale Problems at High Contrast

2016 ◽  
Vol 16 (4) ◽  
pp. 579-603 ◽  
Author(s):  
Daniel Peterseim ◽  
Robert Scheichl
Keyword(s):  
Diffusion Coefficient ◽  
Orthogonal Decomposition ◽  
High Contrast ◽  
Approximation Properties ◽  
New Approach ◽  
Multiscale Problems ◽  
Optimal Convergence ◽  
Discretization Schemes ◽  
Interpolation Operators ◽  
New Framework

AbstractWe present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of ${H^{1}}$ into the image and the kernel of some novel stable quasi-interpolation operators with local $L^{2}$-approximation properties, independent of the contrast. We identify a set of sufficient assumptions on these quasi-interpolation operators that guarantee in principle optimal convergence without pre-asymptotic effects for high-contrast coefficients. We then give an example of a suitable operator and establish the assumptions for a particular class of high-contrast coefficients. So far this is not possible without any pre-asymptotic effects, but the optimal convergence is independent of the contrast and the asymptotic range is largely improved over other discretization schemes. The new framework is sufficiently flexible to allow also for other choices of quasi-interpolation operators and the potential for fully robust numerical upscaling at high contrast.

scholarly journals Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra

2020 ◽  
Vol 30 (09) ◽  
pp. 1809-1855
Author(s):  
Daniele A. Di Pietro ◽  
Jérôme Droniou ◽  
Francesca Rapetti
Keyword(s):  
Finite Element ◽  
Commutative Diagram ◽  
Three Dimensional ◽  
Computer Implementation ◽  
Approximation Properties ◽  
Arbitrary Degree ◽  
Fully Discrete ◽  
De Rham ◽  
Interpolation Operators ◽  
Suitable Approximation

In this work, merging ideas from compatible discretisations and polyhedral methods, we construct novel fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. The spaces and operators that appear in these sequences are directly amenable to computer implementation. Besides proving the exactness, we show that the usual three-dimensional sequence of trimmed Finite Element (FE) spaces forms, through appropriate interpolation operators, a commutative diagram with our sequence, which ensures suitable approximation properties. A discussion on reconstructions of potentials and discrete [Formula: see text]-products completes the exposition.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

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