Research output: Contribution to journal › Article › peer-review
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.
In: Numerical Analysis and Applications, Vol. 17, No. 2, 06.2024, p. 116-131.Research output: Contribution to journal › Article › peer-review
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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