1969/01/01 by Seymour Haber · 1 citation
Mathematics · #Mathematical Approximation and Integration #Statistical and numerical algorithms #Mathematical functions and polynomials
paper · pdf · doi:10.1090/s0025-5718-1969-0260139-1
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.