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.

**[1]**P. J. Davis, ``A construction of nonnegative approximate quadratures,''*Math. Comp.*, v. 21, 1967, pp. 578-587. MR**36**#5584. MR**0222534 (36:5584)****[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)****[5]**A. H. Stroud & D. Secrest,*Gaussian Quadrature Formula*, Prentice-Hall, Englewood Cliffs, N. J., 1966. MR**34**#2185. MR**0202312 (34:2185)****[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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DOI:
https://doi.org/10.1090/S0025-5718-1969-0242374-1

Article copyright:
© Copyright 1969
American Mathematical Society