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Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample. / Voytishek, A. V.; Shlimbetov, N. Kh.

в: Numerical Analysis and Applications, Том 17, № 2, 06.2024, стр. 116-131.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Voytishek, AV & Shlimbetov, NK 2024, 'Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample', Numerical Analysis and Applications, Том. 17, № 2, стр. 116-131. https://doi.org/10.1134/S1995423924020022

APA

Voytishek, A. V., & Shlimbetov, N. K. (2024). Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample. Numerical Analysis and Applications, 17(2), 116-131. https://doi.org/10.1134/S1995423924020022

Vancouver

Voytishek AV, Shlimbetov NK. Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample. Numerical Analysis and Applications. 2024 июнь;17(2):116-131. doi: 10.1134/S1995423924020022

Author

Voytishek, A. V. ; Shlimbetov, N. Kh. / Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample. в: Numerical Analysis and Applications. 2024 ; Том 17, № 2. стр. 116-131.

BibTeX

@article{3a18537d526949ee94a231a5d4452ffe,
title = "Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample",
abstract = "Abstract: In this paper we formulate requirements for choosing approximation bases when constructing cost-effective optimized computational (numerical) functional algorithms for approximating probability densities on the basis of a given sample, with special attention paid to the stability and approximation of the bases. It is shown that to meet the requirements and construct efficient approaches to conditional optimization of numerical schemes, the best choice is a multi-linear approximation and the corresponding special case for both kernel and projection computational algorithms for nonparametric density estimation, which is a multidimensional analogue of the frequency polygon.",
keywords = "Strang–Fix approximation, computational functional kernel algorithm, computational functional projection algorithm, computational nonparametric estimation of probability density on the basis of a given sample, conditional optimization of computational functional algorithms, multi-dimensional analogue of frequency polygon, multi-linear approximation",
author = "Voytishek, {A. V.} and Shlimbetov, {N. Kh}",
year = "2024",
month = jun,
doi = "10.1134/S1995423924020022",
language = "English",
volume = "17",
pages = "116--131",
journal = "Numerical Analysis and Applications",
issn = "1995-4239",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample

AU - Voytishek, A. V.

AU - Shlimbetov, N. Kh

PY - 2024/6

Y1 - 2024/6

N2 - Abstract: In this paper we formulate requirements for choosing approximation bases when constructing cost-effective optimized computational (numerical) functional algorithms for approximating probability densities on the basis of a given sample, with special attention paid to the stability and approximation of the bases. It is shown that to meet the requirements and construct efficient approaches to conditional optimization of numerical schemes, the best choice is a multi-linear approximation and the corresponding special case for both kernel and projection computational algorithms for nonparametric density estimation, which is a multidimensional analogue of the frequency polygon.

AB - Abstract: In this paper we formulate requirements for choosing approximation bases when constructing cost-effective optimized computational (numerical) functional algorithms for approximating probability densities on the basis of a given sample, with special attention paid to the stability and approximation of the bases. It is shown that to meet the requirements and construct efficient approaches to conditional optimization of numerical schemes, the best choice is a multi-linear approximation and the corresponding special case for both kernel and projection computational algorithms for nonparametric density estimation, which is a multidimensional analogue of the frequency polygon.

KW - Strang–Fix approximation

KW - computational functional kernel algorithm

KW - computational functional projection algorithm

KW - computational nonparametric estimation of probability density on the basis of a given sample

KW - conditional optimization of computational functional algorithms

KW - multi-dimensional analogue of frequency polygon

KW - multi-linear approximation

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85195144248&origin=inward&txGid=d88d10b12b873ce177bed76a7e787fd6

UR - https://www.mendeley.com/catalogue/7f1b5edd-af50-3e84-b7a5-c55114b54cf0/

U2 - 10.1134/S1995423924020022

DO - 10.1134/S1995423924020022

M3 - Article

VL - 17

SP - 116

EP - 131

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 2

ER -

ID: 61117416