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Generalized Gauss–Radau and Gauss–Lobatto Formulae

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Abstract

Computational methods are developed for generating Gauss-type quadrature formulae having nodes of arbitrary multiplicity at one or both end points of the interval of integration. Positivity properties of the boundary weights are investigated numerically, and related conjectures are formulated. Applications are made to moment-preserving spline approximation.

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References

  1. W. Gautschi, Orthogonal Polynomials: Computation and Approximation, Numerical Mathematics and Scientific Computation, Oxford University Press, Oxford, 2004.

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  2. W. Gautschi and S. Li, Gauss–Radau and Gauss–Lobatto quadratures with double end points, J. Comput. Appl. Math., 34 (1991), pp. 343–360.

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Authors and Affiliations

  1. Department of Computer Sciences, Purdue University, West Lafayette, IN, 47907, USA

    Walter Gautschi

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  1. Walter Gautschi
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Correspondence to Walter Gautschi.

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AMS subject classification (2000)

65D32, 41A15.

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Gautschi, W. Generalized Gauss–Radau and Gauss–Lobatto Formulae. Bit Numer Math 44, 711–720 (2004). https://doi.org/10.1007/s10543-004-3812-0

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  • DOI: https://doi.org/10.1007/s10543-004-3812-0

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