On the convergence of the quasi-periodic approximations on a finite interval

Armenian Journal of Mathematics

article

Arnak Poghosyan¹  Lusine Poghosyan¹  Rafayel Barkhudaryan² 

[1] Institute of Mathematics;Institute of Mathematics, NAS RA, Yerevan State University

关键词: Truncated Fourier series;    convergence acceleration;    quasi-periodic interpolation;    quasi-periodic approximation;   

DOI  :  10.52737/18291163-2021.13.10-1-44

学科分类：环境科学（综合）

来源: National Academy of Sciences of the Republic of Armenia

【 摘 要 】

We investigate the convergence of the quasi-periodic approximations in different frameworks and reveal exact asymptotic estimates of the corresponding errors. The estimates facilitate a fair comparison of the quasi-periodic approximations to other classical well-known approaches. We consider a special realization of the approximations by the inverse of the Vandermonde matrix, which makes it possible to prove the existence of the corresponding implementations, derive explicit formulas and explore convergence properties. We also show the application of polynomial corrections for the convergence acceleration of the quasi-periodic approximations. Numerical experiments reveal the auto-correction phenomenon related to the polynomial corrections so that utilization of approximate derivatives surprisingly results in better convergence compared to the expansions with the exact ones.

【 授权许可】

CC BY