Stochastic quadrature formulas
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- by Seymour Haber PDF
- Math. Comp. 23 (1969), 751-764 Request permission
Corrigendum: Math. Comp. 24 (1970), 1001.
Corrigendum: Math. Comp. 24 (1970), 1001.
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.References
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Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Math. Comp. 23 (1969), 751-764
- MSC: Primary 65.15
- DOI: https://doi.org/10.1090/S0025-5718-1969-0260139-1
- MathSciNet review: 0260139