On a Pointwise Convergence of Quasi-Periodic-Rational Trigonometric Interpolation

Poghosyan, Arnak; Poghosyan, Lusine

doi:10.1155/2014/249513

Cited by 6 publications

(9 citation statements)

References 4 publications

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“…It means that m = 1 of the QP-interpolation corresponds to m = 0 of the QP-approximation. The next theorem, proved in [91], revealed the convergence rate of the QP-interpolation, where i N,m (f, x) corresponded to the error of the QP-interpolation.…”

Section: The Pointwise Convergencementioning

confidence: 94%

“…Let us compare the behaviors of the quasi-periodic approximations (Algorithm C) and interpolations (see [94,95]). The QP-approximation is written via Vandermonde matrix (12) of size (2m + 2) × (2m + 2), where (2m + 2) is the number of points outside of [−1, 1] used for extensions.…”

Section: The Pointwise Convergencementioning

confidence: 99%

“…We will refer to this approach as the Krylov-Lanczos method. Jones and Hardy [60] and Lyness [61] considered convergence acceleration of trigonometric interpolations by the polynomial subtraction (see also [62,63]).…”

Section: Introductionmentioning

confidence: 99%

“…That is why those expansions were called as quasi-periodic (QP-) interpolations. Let us introduce the idea of [90] in more details (see also [91]). Consider a new function g(t) defined on [−σ, σ] by the following change of variable…”

Section: Introductionmentioning

confidence: 99%

“…This non-uniformity should be one of the main reasons of better convergence properties of the QP-interpolation compared to the classical trigonometric interpolation that uses uniform grids. Papers [91][92][93][94][95] investigated the pointwise convergence of the QP-interpolation and its convergence in the L 2 -norm. The application of polynomial corrections to the QP-interpolation was considered in [95] for complete elimination of the Gibbs phenomenon and additional convergence acceleration.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Poghosyan

Barkhudaryan

2021

Armen. J. Math.

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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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Section: The Pointwise Convergencementioning

confidence: 94%

Section: The Pointwise Convergencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Poghosyan

Barkhudaryan

2021

Armen. J. Math.

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On Some Fast Implementations of Fourier Interpolation

Nersessian

2021

Operator Theory and Harmonic Analysis

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Non‐residents’ Holdings, Market Volatility and Public Debt Sustainability. An Analysis with Data for Italy

Cafiso

2016

Rev International Economics

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Non-residents' holdings (NRH) of debt securities have been large in euro area countries, but during the euro area debt crisis some of those countries experienced a steep contraction of such holdings. The analysis aims to provide a data-founded explanation of what is behind the decrease observed in 2011 by testing two alternative hypotheses. At the same time, we discuss how that decrease might have endangered the sustainability of public debt and study the empirical relevance of the most important of those processes. The topics presented refer to any advanced economy, but we check the hypotheses discussed by taking Italy as a case study because of data constraints. Italy is an interesting country to consider since it is a very large debt issuer. Our results point towards the importance of market volatility to explain variations of NRH, but those holdings do not seem to influence debt sustainability.Non-residents' holdings of public debt within the EA have been favored by the introduction of the common currency in 1999 (Lane, 2006), which boosted demand for NON-RESIDENTS' HOLDINGS AND PUBLIC DEBT 485

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On a Pointwise Convergence of Quasi-Periodic-Rational Trigonometric Interpolation

Cited by 6 publications

References 4 publications

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

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

On Some Fast Implementations of Fourier Interpolation

Non‐residents’ Holdings, Market Volatility and Public Debt Sustainability. An Analysis with Data for Italy

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