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A129337
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Maximal possible degree of a Chebyshev-type quadrature formula with n nodes, in the case of the constant weight function on [ -1,1].
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0
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1, 3, 3, 5, 5, 7, 7, 7, 9, 9, 9, 9, 11, 11, 11, 11, 13, 13, 13, 13, 13, 15, 15, 15, 15
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OFFSET
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1,2
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COMMENTS
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These are the results reported in reference [1]. Spherical designs in 3 dimensions (cf. A007828) also project to Chebyshev-type quadrature rules for the constant weight function on [ -1,1] (see reference [2]), but apparently this yields a smaller maximum degree for any given n.
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REFERENCES
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[1] Klaus-Jurgen Forster and Georg-Peter Ostermeyer, On Weighted Chebyshev-Type Quadrature Formulas, Mathematics of Computation, Vol. 46, No. 174. (Apr., 1986), pp. 591-599. Table 1, p. 596.
[2] Greg Kuperberg, Numerical Cubature from Archimedes' Hat-box Theorem, SIAM J. Numer. Anal. 44 (2006), no. 3, 908--935.
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LINKS
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Table of n, a(n) for n=1..25.
Klaus-Jurgen Forster, Georg-Peter Ostermeyer, On Weighted Chebyshev-Type Quadrature Formulas,Mathematics of Computation, Vol. 46, No. 174. (Apr., 1986), pp. 591-599. Table 1, p. 596.
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CROSSREFS
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Cf. A007828.
Sequence in context: A078936 A061794 A088524 * A133909 A177691 A206913
Adjacent sequences: A129334 A129335 A129336 * A129338 A129339 A129340
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KEYWORD
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more,nonn
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AUTHOR
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Paul Leopardi, May 28 2007
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STATUS
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approved
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