scholarly journals On mean approximation of function and its derivatives

2018 ◽  
Vol 26 (1) ◽  
pp. 56
Author(s):  
V.P. Motornyi
Keyword(s):  
Approximation Of Function

Some properties of the functions being integrable on the segment were considered in this article. Estimates for approximation are obtained.

scholarly journals Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays

2009 ◽  
Vol 31 (4) ◽  
pp. 3002-3026 ◽  
Author(s):  
B. N. Khoromskij ◽  
V. Khoromskaia
Keyword(s):  
Multidimensional Arrays ◽  
Tensor Approximation ◽  
Approximation Of Function

scholarly journals PRIVACY PRESERVING CLUSTERING BASED ON LINEAR APPROXIMATION OF FUNCTION

2013 ◽  
Vol 12 (5) ◽  
pp. 3443-3451
Author(s):  
Rajesh Pasupuleti ◽  
Narsimha Gugulothu
Keyword(s):  
Linear Approximation ◽  
Clustering Algorithms ◽  
Similarity Measures ◽  
Privacy Preserving ◽  
Distance Measures ◽  
Clustering Methods ◽  
Sensitive Data ◽  
Processing Information ◽  
Data Objects ◽  
Approximation Of Function

Clustering analysis initiatives  a new direction in data mining that has major impact in various domains including machine learning, pattern recognition, image processing, information retrieval and bioinformatics. Current clustering techniques address some of the  requirements not adequately and failed in standardizing clustering algorithms to support for all real applications. Many clustering methods mostly depend on user specified parametric methods and initial seeds of clusters are randomly selected by  user.  In this paper, we proposed new clustering method based on linear approximation of function by getting over all idea of behavior knowledge of clustering function, then pick the initial seeds of clusters as the points on linear approximation line and perform clustering operations, unlike grouping data objects into clusters by using distance measures, similarity measures and statistical distributions in traditional clustering methods. We have shown experimental results as clusters based on linear approximation yields good  results in practice with an example of  business data are provided.  It also  explains privacy preserving clusters of sensitive data objects.

Optimal Approximation of Function and Integration on Some Analytic Classes

2011 ◽  
Vol 10 (11) ◽  
pp. 2196-2201
Author(s):  
Ye Peixin ◽  
Li Xuehua
Keyword(s):  
Optimal Approximation ◽  
Approximation Of Function

On orders of approximation of function classes in Lorentz spaces with anisotropic norm

2007 ◽  
Vol 81 (1-2) ◽  
pp. 3-14
Author(s):  
G. A. Akishev
Keyword(s):  
Lorentz Spaces ◽  
Function Classes ◽  
Anisotropic Norm ◽  
Approximation Of Function

scholarly journals One counterexample for convex approximation of function with fractional derivatives, r>4

2018 ◽  
pp. 53-56
Author(s):  
T. Petrova
Keyword(s):  
Convex Function ◽  
Algebraic Polynomial ◽  
Fractional Derivatives ◽  
Nondecreasing Function ◽  
Degree Of Approximation ◽  
Monotone Approximation ◽  
Convex Approximation ◽  
Positive Functions ◽  
Approximation Of A Function ◽  
Approximation Of Function

We discuss whether on not it is possible to have interpolatory estimates in the approximation of a function f \in W^r [0,1] by polynomials. The problem of positive approximation is to estimate the pointwise degree of approximation of a function f \in C^r [0,1] \Wedge \Delta^0, where \Delta^0 is the set of positive functions on [0,1]. Estimates of the form (1) for positive approximation are known ([1],[2]). The problem of monotone approximation is that of estimating the degree of approximation of a monotone nondecreasing function by monotone nondecreasing polynomials. Estimates of the form (1) for monotone approximation were proved in [3],[4],[8]. In [3],[4] is consider r \in N, r>2. In [8] is consider r \in R, r>2. It was proved that for monotone approximation estimates of the form (1) are fails for r \in R, r>2. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is consider in ([5],[6],[11]). In [5] is consider r \in N, r>2. It was proved that for convex approximation estimates of the form (1) are fails for r \in N, r>2. In [6] is consider r \in R, r\in(2;3). It was proved that for convex approximation estimates of the form (1) are fails for r \in R, r\in(2;3). In [11] is consider r \in R, r\in(3;4). It was proved that for convex approximation estimates of the form (1) are fails for r \in R, r\in(3;4). In [9] is consider r \in R, r>4. It was proved that for f \in W^r [0,1] \Wedge \Delta^2, r>4 estimate (1) is not true. In this paper the question of approximation of function f \in W^r [0,1] \Wedge \Delta^2, r>4 by algebraic polynomial p_n \in \Pi_n \Wedge \Delta^2 is consider. It is proved, that for f \in W^r [0,1] \Wedge \Delta^2, r>4, estimate (1) can be improved, generally speaking.

scholarly journals On degree of approximation of Fourier series of functions in Besov space using Norlund meanIn the present article, we have established a result on degree of approximation of function in the Besov space by (N; rn)- mean of  Trigonometric Fourier series

2021 ◽  
Author(s):  
Birupakhya Prasad Padhy ◽  
Anwesha Mishra ◽  
U. K. Misra
Keyword(s):  
Fourier Series ◽  
Present Article ◽  
Besov Space ◽  
Degree Of Approximation ◽  
Trigonometric Fourier Series ◽  
Series Of Functions ◽  
Approximation Of Function

In the present article, we have established a result on degree of approximation of function in the Besov space by (N; rn)- mean of  Trigonometric Fourier series

Approximation of Function Defined on Full Axis of Real by a Class of Neural Networks: Density, Complexity and Constructive Algorithm

2012 ◽  
Vol 35 (4) ◽  
pp. 786-795
Author(s):  
Fei-Long CAO ◽  
Zhen-Cai LI ◽  
Jian-Wei ZHAO ◽  
Ke LV
Keyword(s):  
Neural Networks ◽  
Constructive Algorithm ◽  
Approximation Of Function

Degree of Approximation of Function in the Holder Metric by (N,Pn) (E,q) Means

2019 ◽  
Vol 65 (4) ◽  
pp. 101-106
Author(s):  
Santosh Kumar Sinha ◽  
Shrivastava U.K
Keyword(s):  
Degree Of Approximation ◽  
Hölder Metric ◽  
Approximation Of Function
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