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

Nersessian, A.; Poghosyan, A.

J. Sci. Comput. 26, No. 1, 111-125 (2006).

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.

Reviewer: Vladimir N. Karpushkin (Moskva)

MSC:

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

Keywords:

Fourier series; Padé approximation; rational approximations

Citations:

Zbl 0973.65133

References:

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