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A general algorithm for nonnegative quadrature formulas


Author: M. Wayne Wilson
Journal: Math. Comp. 23 (1969), 253-258
MSC: Primary 65.55
DOI: https://doi.org/10.1090/S0025-5718-1969-0242374-1
MathSciNet review: 0242374
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Abstract: A general algorithm is presented for determining numerical integration formulas exact for an arbitrary finite set of continuous functions defined on a compact set, involving nonnegative combinations of function values at a finite number of points in the set. Examples are given.


References [Enhancements On Off] (What's this?)

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  • [2] P. J. Davis, ``Approximate integration rules with nonnegative weights,'' in Lecture Series in Differential Equations, Georgetown University, Washington, D. C., 1967.
  • [3] W. Fraser & M. W. Wilson, ``Remarks on the Clenshaw-Curtis quadrature scheme,'' SI AM Rev., v. 8, 1966, pp. 322-327. MR 34 #3784. MR 0203937 (34:3784)
  • [4] W. W. Rogosinski, ``On non-negative polynomials,'' Ann. Univ. Sci. Budapest, Eötvös Sect. Math., v. 3-4, 1961, pp. 253-280. MR 26 #3843. MR 0146321 (26:3843)
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  • [6] V. Tchakaloff, ``Formules de cubatures mécaniques à coefficients non-négatifs,'' Bull. Sci. Math., (2) v. 81, 1957, pp. 123-134. MR 20 #1145. MR 0094632 (20:1145)
  • [7] M. W. Wilson, Geometric Aspects of Quadratures with Non-Negative Weights, Ph.D. Thesis, Brown University, 1968.
  • [8] M. W. Wilson, Approximation of Non-Negative Continuous Linear Functionals, Brown University Technical Report, May, 1968.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0242374-1
Article copyright: © Copyright 1969 American Mathematical Society

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