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Orthogonal rational functions on a semi-infinite interval. (English) Zbl 0614.42013

The author obtains a sequence of orthogonal functions on [0,\(\infty [\) by taking a Möbius transform in the argument of the usual Chebyshev polynomials. He discusses their applicability to expansions of functions, solution of eigenproblems, and boundary value problems in seven numerical examples.
Reviewer: J.Karlsson

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
41A20 Approximation by rational functions
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References:

[1] Boyd, J. P., J. Comput. Phys., 69, 112-142 (1987)
[2] Grosch, C. E.; Orszag, S. A., J. Comp. Phys., 25, 273 (1977)
[3] Boyd, J. P., J. Comput. Phys., 45, 43 (1982)
[4] Boyd, J. P., J. Comput. Phys., 54, 382 (1984)
[5] Boyd, J. P., J. Comput. Phys., 57, 454 (1985)
[6] Boyd, J. P., J. Comput. Phys., 64, 266 (1986)
[7] Norton, H. J., Comput. J., 7, 76 (1964)
[8] Boyd, J. P., Physica D, 21, 227 (1986)
[9] Gottlieb, D.; Orszag, S. A., Numerical Analysis of Spectral Methods: Theory and Applications (1977), SIAM Philadelphia · Zbl 0412.65058
[10] Cain, A. B.; Ferziger, J. H.; Reynolds, W. C., J. Comput. Phys., 56, 272 (1984)
[11] Boyd, J. P., Monthly Weather Rev., 106, 1192 (1978)
[12] Pedlosky, J., Geophysical Fluid Dynamics (1979), Springer-Verlag: Springer-Verlag New York · Zbl 0429.76001
[13] Boyd, J. P., J. Math. Phys., 19, 1445 (1978)
[14] Stenger, F., SIAM Rev., 23, 165 (1981)
[15] Nayfeh, A. H., Perturbation Methods (1973), Wiley: Wiley New York · Zbl 0375.35005
[16] Canuto, C.; Quarteroni, A., J. Comput. Phys., 60, 315 (1985)
[17] Boyd, J. P., J. Sci. Comput., 1, 183 (1986)
[18] Gary, J.; Helgason, R., J. Comput. Phys., 5, 169 (1970)
[19] Trefethen, L. N.; Trummer, M. R., SIAM J. Numer. Anal. (1986), in press
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