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Suboptimality of Gauss–Hermite Quadrature and Optimality of the Trapezoidal Rule for Functions with Finite Smoothness
The suboptimality of Gauss–Hermite quadrature and the optimality of the trapezoidal rule are proved in the weighted Sobolev spaces of square integrable functions of order , where the optimality is in the sense of worst-case error. For Gauss–Hermite quadrature, we obtain matching lower and upper bounds, which turn out to …