On a Rational Linear Approximation of Fourier Series for Smooth Functions

Authors:
A. Nersessian;A. Poghosyan
Affiliations:
National Academy of Sciences of Armenia, Institute of Mathematics, Yerevan, Armenia 375019;National Academy of Sciences of Armenia, Institute of Mathematics, Yerevan, Armenia 375019
Venue:
Journal of Scientific Computing
Year:
2006

Citing 8
Cited 1

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The Mathematica book (4th edition)

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ON THE GIBBS PHENOMENON III: RECOVERING EXPONENTIAL ACCURACY IN A SUB-INTERVAL FROM A SPECTRAL PARTIAL SUM OF A PIECEWISE ANALYTIC FUNCTION

ON THE GIBBS PHENOMENON III: RECOVERING EXPONENTIAL ACCURACY IN A SUB-INTERVAL FROM A SPECTRAL PARTIAL SUM OF A PIECEWISE ANALYTIC FUNCTION

Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of 1/n

Journal of Computational Physics

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Abstract

The Fourier series of a smooth function on a compact interval usually has slow convergence due to the Gibbs phenomena. A class of Fourier-Pade approximations is introduced and studied for performing a boundary correction. Additional acceleration is achieved by applying Fourier---Bernoulli scheme.