TY - JOUR

T1 - Approximation and Smoothing of Functions Based on Godunov Regularization

AU - Biberdorf, E. A.

AU - Abdisheripov, K. K.

N1 - This work was accomplished within the state assignment of the Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0008 and the Foundation El-yurt umidi, Uzbekistan.

PY - 2024/8

Y1 - 2024/8

N2 - A new approach to function approximation is presented based on the ideas of S.K. Godunov on the regularization of ill-conditioned systems. The proposed method makes it possible to determine the values of functions at fine grid nodes based on data from a larger grid, while providing control over the smoothness of the resulting function. The estimates of convergence and smoothness are substantiated, and the results of computational experiments are presented illustrating the effectiveness of the proposed method.

AB - A new approach to function approximation is presented based on the ideas of S.K. Godunov on the regularization of ill-conditioned systems. The proposed method makes it possible to determine the values of functions at fine grid nodes based on data from a larger grid, while providing control over the smoothness of the resulting function. The estimates of convergence and smoothness are substantiated, and the results of computational experiments are presented illustrating the effectiveness of the proposed method.

KW - approximation

KW - regularization of ill-conditioned SLAEs

KW - smoothing of functions

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85205314396&origin=inward&txGid=d0b815a77b5d326ef6753d7d12d511ff

UR - https://www.mendeley.com/catalogue/f31d00cf-268b-384b-8a52-d0237d93ffe1/

U2 - 10.1134/S0965542524700799

DO - 10.1134/S0965542524700799

M3 - Article

VL - 64

SP - 1653

EP - 1666

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 8

ER -