论文信息 - Error expansions for multidimensional trapezoidal rules with Sidi transformations

Error expansions for multidimensional trapezoidal rules with Sidi transformations

In 1993, Sidi introduced a set of trigonometric transformations x = ψ(t) that improve the effectiveness of the one-dimensional trapezoidal quadrature rule for a finite interval. In this paper, we extend Sidi's approach to product multidimensional quadrature over [0,1]N. We establish the Euler–Maclaurin expansion for this rule, both in the case of a regular integrand function f(x) and in the cases when f(x) has homogeneous singularities confined to vertices.

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