Armenian Journal of Mathematics, 13(10)
2021; 1–44
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On the convergence of the quasi-periodic approximations on a finite interval

Arnak Poghosyan*, Lusine Poghosyan, Rafayel Barkhudaryan

Received: 2024-12-07 · Published: 2021-12-10

© 2021 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
On the convergence of the quasi-periodic approximations on a finite interval
Authors
Arnak Poghosyan, Lusine Poghosyan, Rafayel Barkhudaryan
Source journal
Armenian Journal of Mathematics, 13(10)
Published
2021-12-10
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2021.13.10-1-44

Abstract

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.
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