On a rational linear approximation of Fourier series for smooth functions. (English) Zbl 1114.41008

The topic of the paper is to improve the convergence of the Fourier series, a branch of numerical analysis. It is stated that the Fourier series of functions of \(p\)-derivatives \((p\geq 0)\) with discontinuities have slow convergence on the approximation interval because of the Gibbs phenomena. Referring to many works on this subject, the authors would propose a class of Fourier-Padé approximation to “eliminate” the Gibbs phenomena [see T. A. Driscoll and B. Fornberg, Numer. Algorithms 26, No. 1, 77–92 (2001; Zbl 0973.65133)]. A theorem developing convergence degree is proved. Numerical examples are given. There is a lot of bibliography.


41A21 Padé approximation
65T40 Numerical methods for trigonometric approximation and interpolation
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series


Zbl 0973.65133
Full Text: DOI


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