Stochastic quadrature formulas

Haber, Seymour

doi:10.1090/S0025-5718-1969-0260139-1

Stochastic quadrature formulas

Author: Seymour Haber
Journal: Math. Comp. 23 (1969), 751-764
MSC: Primary 65.15
DOI: https://doi.org/10.1090/S0025-5718-1969-0260139-1
Corrigendum: Math. Comp. 24 (1970), 1001.
Corrigendum: Math. Comp. 24 (1970), 1001.
MathSciNet review: 0260139
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Abstract: A class of formulas for the numerical evaluation of multiple integrals is described, which combines features of the Monte-Carlo and the classical methods. For certain classes of functions--defined by smoothness conditions--these formulas provide the fastest possible rate of convergence to the integral. Asymptotic error estimates are derived, and a method is described for obtaining good a posteriori error bounds when using these formulas. Equal-coefficients formulas of this class, of degrees up to 3, are constructed.

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