scholarly journals Chebyshev approximation of functions of two variables by a rational expression with interpolation

2021 ◽  
pp. 33-39
Author(s):  
Lev Melnychok
Keyword(s):  
Least Squares Method ◽  
Iterative Scheme ◽  
Chebyshev Approximation ◽  
Weight Functions ◽  
Approximation Of Functions ◽  
Mean Power ◽  
Rational Expression ◽  
Functions Of Two Variables ◽  
Power Approximation ◽  
Variable Weight

A method for constructing a Chebyshev approximation by a rational expression with interpolation for functions of two variables is proposed The idea of the method is based on the construction of the ultimate mean-power approximation in the norm of space Lp at p° . An iterative scheme based on the least squares method with two variable weight functions was used to construct such a Chebyshev approximation. The results of test examples confirm the effectiveness of the proposed method for constructing the Chebyshev approximation by a rational expression with interpolation.

scholarly journals Chebyshev approximation of the multivariable functions by some nonlinear expressions

2021 ◽  
pp. 18-22
Author(s):  
Petro Malachivskyy
Keyword(s):  
Weight Function ◽  
Least Squares ◽  
Iterative Scheme ◽  
Chebyshev Approximation ◽  
Method Of Least Squares ◽  
Functional Transformation ◽  
Generalized Polynomial ◽  
Variable Weight

A method for constructing a Chebyshev approximation of the multivariable functions by exponential, logarithmic and power expressions is proposed. It consists in reducing the problem of the Chebyshev approximation by a nonlinear expression to the construction of an intermediate Chebyshev approximation by a generalized polynomial. The intermediate Chebyshev approximation by a generalized polynomial is calculated for the values of a certain functional transformation of the function we are approximating. The construction of the Chebyshev approximation of the multivariable functions by a polynomial is realized by an iterative scheme based on the method of least squares with a variable weight function.

scholarly journals Chebyshev Approximation by Rational Expression Functions of Two Variables

2019 ◽  
pp. 75-81
Author(s):  
P. S. Malachivskyy ◽  
◽  
B. R. Montsibovych ◽  
Ya. V. Pizyur ◽  
R. P. Malachivskyi ◽  
...  
Keyword(s):  
Chebyshev Approximation ◽  
Rational Expression ◽  
Functions Of Two Variables

scholarly journals Chebyshev approximation of functions of two variables with interpolation

2019 ◽  
Vol 2 (42) ◽  
pp. 38-47
Author(s):  
P. S. Malachivskyy ◽  
◽  
L. S. Melnychok ◽  
Ya. V. Pizyur ◽  
◽  
...  
Keyword(s):  
Chebyshev Approximation ◽  
Approximation Of Functions ◽  
Functions Of Two Variables

Chebyshev Approximation by a Rational Expression for Functions of Many Variables

2020 ◽  
Vol 56 (5) ◽  
pp. 811-819
Author(s):  
P. S. Malachivskyy ◽  
Ya. V. Pizyur ◽  
R. P. Malachivsky
Keyword(s):  
Chebyshev Approximation ◽  
Rational Expression

Grey cluster evaluation models based on mixed triangular whitenization weight functions

2015 ◽  
Vol 5 (3) ◽  
pp. 410-418 ◽  
Author(s):  
Si-feng Liu ◽  
Yingjie Yang ◽  
Zhi-geng Fang ◽  
Naiming Xie
Keyword(s):  
Weight Function ◽  
Evaluation Model ◽  
Weight Functions ◽  
The Novel ◽  
Content Type ◽  
Clustering Model ◽  
Cluster Evaluation ◽  
Fixed Weight ◽  
Variable Weight ◽  
Evaluation Models

Purpose – The purpose of this paper is to present two novel grey cluster evaluation models to solve the difficulty in extending the bounds of each clustering index of grey cluster evaluation models. Design/methodology/approach – In this paper, the triangular whitenization weight function corresponding to class 1 is changed to a whitenization weight function of its lower measures, and the triangular whitenization weight function corresponding to class s is changed to a whitenization weight function of its upper measures. The difficulty in extending the bound of each clustering indicator is solved with this improvement. Findings – The findings of this paper are the novel grey cluster evaluation models based on mixed centre-point triangular whitenization weight functions and the novel grey cluster evaluation models based on mixed end-point triangular whitenization weight functions. Practical implications – A practical evaluation and decision problem for some projects in a university has been studied using the new triangular whitenization weight function. Originality/value – Particularly, compared with grey variable weight clustering model and grey fixed weight clustering model, the grey cluster evaluation model using whitenization weight function is more suitable to be used to solve the problem of poor information clustering evaluation. The grey cluster evaluation model using endpoint triangular whitenization weight functions is suitable for the situation that all grey boundary is clear, but the most likely points belonging to each grey class are unknown; the grey cluster evaluation model using centre-point triangular whitenization weight functions is suitable for those problems where it is easier to judge the most likely points belonging to each grey class, but the grey boundary is not clear.

scholarly journals A Meshless Local Petrov-Galerkin Shepard and Least-Squares Method Based on Duo Nodal Supports

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaoying Zhuang ◽  
Yongchang Cai
Keyword(s):  
Least Squares ◽  
Present Method ◽  
Least Squares Method ◽  
Partition Of Unity ◽  
Weak Form ◽  
Weight Functions ◽  
Kronecker Delta ◽  
Background Mesh ◽  
Support Domain ◽  
New Formulation

The meshless Shepard and least-squares (MSLS) interpolation is a newly developed partition of unity- (PU-) based method which removes the difficulties with many other meshless methods such as the lack of the Kronecker delta property. The MSLS interpolation is efficient to compute and retain compatibility for any basis function used. In this paper, we extend the MSLS interpolation to the local Petrov-Galerkin weak form and adopt the duo nodal support domain. In the new formulation, there is no need for employing singular weight functions as is required in the original MSLS and also no need for background mesh for integration. Numerical examples demonstrate the effectiveness and robustness of the present method.

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