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

Authors

  • Arnak Poghosyan Institute of Mathematics, NAS RA
  • Lusine Poghosyan Institute of Mathematics, NAS RA
  • Rafayel Barkhudaryan Institute of Mathematics, NAS RA; Yerevan State University

DOI:

https://doi.org/10.52737/18291163-2021.13.10-1-44

Keywords:

Truncated Fourier series, convergence acceleration, quasi-periodic interpolation, quasi-periodic approximation

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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2021-12-10

How to Cite

Poghosyan, A., Poghosyan, L., & Barkhudaryan, R. (2021). On the convergence of the quasi-periodic approximations on a finite interval. Armenian Journal of Mathematics, 13(10), 1–44. https://doi.org/10.52737/18291163-2021.13.10-1-44

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