A Padé-based algorithm for overcoming the Gibbs phenomenon

Numerical Algorithms

Volumn 26, Issue 1, 2001, Pages 77-92

  Driscoll, Tobin A ^a   Fornberg, Bengt ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

Fourier series; Gibbs phenomenon; Interpolation; Pad approximation

Indexed keywords

EID: 0035635781     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016648530648     Document Type: Article

References (16)

1. G.A. Baker and P. Graves-Morris, Padé Approximants, Encyclopedia of Mathematics and Its Applications, Vol. 59, 2nd ed. (Cambridge Univ. Press, Cambridge, 1996).
2. N.S. Banerjee and J.F. Geer, Exponential approximations using Fourier series partial sums, Technical Report 97-56, ICASE (1997).
3. C. Brezinski, The asymptotic behavior of sequences and new series transformations based on the Cauchy product, Rocky Mountain J. Math. 21 (1991) 71-84.
4. R.G. Brookes, The local behavior of the quadratic Hermite-Padé approximation, in: Computational Techniques and Applications, eds. W.L. Hogarth and B.J. Noye (Hemisphere Publ. Corp., New York, 1990) pp. 569-575.
5. J.S.R. Chisholm and A.K. Common, Generalisations of Padé approximation for Chebyshev and Fourier series, in: E.B. Christoffel: The Influence of His Work on Mathematics and the Physical Sciences, eds. P.L. Butzer and F. Fehér (Birkhäuser, Basel, 1981) pp. 212-231.
6. K.S. Eckhoff, On a high order numerical method for functions with singularities, Math. Comp. 67 (1998) 1063-1087.
7. B. Fornberg, A Practical Guide to Pseudospectral Methods (Cambridge Univ. Press, Cambridge, 1996).
8. J.F. Geer, Rational trigonometric approximations using Fourier series partial sums, J. Sci. Comput. 10 (1995) 325-356.
9. J. Geer and N.S. Banerjee, Exponentially accurate approximations to piecewise smooth periodic functions, J. Sci. Comput. 12 (1997) 253-287.
10. A. Gelb and E. Tadmor, Detection of edges in spectral data, Appl. Comput. Harmon. Anal. 7 (1999) 101-135.
11. D. Gottlieb and C.-W. Shu, On the Gibbs phenomenon and its resolution, SIAM Rev. 39 (1997) 644-668.
12. W.B. Gragg, Laurent, Fourier, and Chebyshev-Padé tables, in: Padé and Rational Approximation, Theory and Applications, eds. E.B. Saff and R.S. Varga (Academic Press, New York, 1977).
13. G. Kvernadze, T. Hagstrom and H. Shapiro, Locating discontinuities of a bounded function by the partial sums of its Fourier series, J. Sci. Comput. 14 (1999) 301-327.
14. G. Kvernadze, Locating discontinuities of a bounded function by spectral methods, Ph.D. thesis, University of New Mexico (1998).
15. R.E. Shafer, On quadratic approximation, SIAM J. Numer. Anal. 11 (1974) 447-460.
16. R.D. Small and R.J. Charron, Continuous and discrete nonlinear approximation based on Fourier series, IMA J. Num. Anal. 8 (1988) 281-293.