scholarly journals On Hermite-Fejér interpolation with equidistant nodes

1990 ◽  
Vol 48 (3) ◽  
pp. 461-471
Author(s):  
G. B. Baker ◽  
T. M. Mills ◽  
P. Vértesi
Keyword(s):  
Interpolation Process ◽  
Infinite Interval ◽  
Approximation Properties ◽  
Interpolation Of Functions ◽  
Equidistant Nodes

AbstractThis paper deals with Hermite-Fejér interpolation of functions defined on a semi-infinite interval but the nodes are equally spaced. It is shown that, under certain conditions, the interpolation process has poor approximation properties.

Stability of Interpolation on an Infinite Interval

1966 ◽  
Vol 9 (05) ◽  
pp. 655-666
Author(s):  
R.B. Saxena
Keyword(s):  
Finite Interval ◽  
Minimal Degree ◽  
Interpolation Process ◽  
Infinite Interval ◽  
The One ◽  
Definition Of ◽  
Suitable Modification

In 1958, Egerváry and Turán [3] proposed and solved the problem of finding a stable interpolation process of minimal degree on a finite interval. Later [4] they investigated the same problem for an infinite interval with a suitable modification of the definition of stability. For the interval (-∞, ∞) their definition naturally differs from the one for the semi-infinite interval.

scholarly journals Generalized Bernstein type operators on unbounded interval and some approximation properties

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2797-2808 ◽  
Author(s):  
Mohd Ahasan ◽  
Faisal Khan ◽  
Mohammad Mursaleen
Keyword(s):  
Exponential Function ◽  
Infinite Interval ◽  
Approximation Properties ◽  
Bernstein Type ◽  
Unbounded Interval ◽  
New Family

In the present paper, we construct a new family of Bernstein type operators on infinite interval by using exponential function ax. We study some approximation results for these new operators on the interval [0,1).

THEORY OF INTERPOLATION ON INFINITE INTERVAL—I

1986 ◽  
Vol 6 (4) ◽  
pp. 373-378
Author(s):  
K.B. Srivastava
Keyword(s):  
Infinite Interval

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.

Approximation properties of Szász type operators involving Charlier polynomials

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 479-487
Author(s):  
Didem Arı
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Approximation Properties ◽  
Charlier Polynomials

In this paper, we give some approximation properties of Sz?sz type operators involving Charlier polynomials in the polynomial weighted space and we give the quantitative Voronovskaya-type asymptotic formula.

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