A general algorithm for nonnegative quadrature formulas

Author:
M. Wayne Wilson

Journal:
Math. Comp. **23** (1969), 253-258

MSC:
Primary 65.55

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]**Philip J. Davis,*A construction of nonnegative approximate quadratures*, Math. Comp.**21**(1967), 578–582. MR**0222534**, 10.1090/S0025-5718-1967-0222534-4**[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 and M. W. Wilson,*Remarks on the Clenshaw-Curtis quadrature scheme*, SIAM Rev.**8**(1966), 322–327. MR**0203937****[4]**W. W. Rogosinski,*On non-negative polynomials*, Ann. Univ. Sci. Budapest. Eötvös Sect. Math.**3-4**(1960/1961), 253–280. MR**0146321****[5]**A. H. Stroud and Don Secrest,*Gaussian quadrature formulas*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR**0202312****[6]**Vladimir Tchakaloff,*Formules de cubatures mécaniques à coefficients non négatifs*, Bull. Sci. Math. (2)**81**(1957), 123–134 (French). MR**0094632****[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:
http://dx.doi.org/10.1090/S0025-5718-1969-0242374-1

Article copyright:
© Copyright 1969
American Mathematical Society