On the Convergence of the Quasi-Periodic Approximations on a Finite Interval

IF 0.5 Q3 MATHEMATICS Armenian Journal of Mathematics Pub Date : 2021-12-10 DOI:10.52737/18291163-2021.13.10-1-44
A. Poghosyan, Lusine Poghosyan, R. Barkhudaryan
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引用次数: 1

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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有限区间上拟周期逼近的收敛性
研究了拟周期逼近在不同框架下的收敛性,并给出了相应误差的精确渐近估计。这些估计有助于将拟周期近似与其他经典的众所周知的方法进行公平的比较。我们考虑了Vandermonde矩阵逆逼近的一种特殊实现,从而证明了相应实现的存在性,推导了显式公式,并探讨了收敛性。我们还展示了多项式修正在拟周期逼近收敛加速中的应用。数值实验揭示了与多项式修正相关的自动修正现象,因此使用近似导数比使用精确导数展开式具有更好的收敛性。
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来源期刊
CiteScore
0.60
自引率
0.00%
发文量
13
审稿时长
48 weeks
期刊最新文献
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