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Numerical integration rules near gaussian quadrature

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Abstract

We call a numerical integration formula based onk nodes which is exact for polynomials of degree at mostn an (n, k) formula. Gaussian quadrature is the unique (2k−1,k) formula. In this paper we give a complete description of all (2k−3,k) formulas, including a characterization of those having all positive weights.

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References

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Authors and Affiliations

  1. IBM Research Center, Yorktown Heights, New York, U.S.A.

    C. A. Micchelli & T. J. Rivlin

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  1. C. A. Micchelli
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  2. T. J. Rivlin
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Dedicated to Professor I. J. Schoenberg on the occasion of his seventieth birthday.

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Micchelli, C.A., Rivlin, T.J. Numerical integration rules near gaussian quadrature. Israel J. Math. 16, 287–299 (1973). https://doi.org/10.1007/BF02756708

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  • DOI: https://doi.org/10.1007/BF02756708

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