SHARP ERROR BOUNDS FOR THE TRAPEZOIDAL RULE AND SIMPSON'S RULE

2002

79 citations recorded by the source corpus.

Citations in the corpus

• On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions (2015, neutral): “r Simpson’s rules, which are based on interpolation between the sample points, and for which the error decays as O(1/n2) and O(1/n4) for functions with uniformly bounded second or fourth derivatives (Cruz-Uribe and Neugebauer, 2002). Gaussian quadrature is another class of methods for one-dimensiona”
• On the Equivalence between Quadrature Rules and Random Features (2015, unknown): “…line, several methods exists, such as the trapezoidal or Simpson’s rules, which are based on interpolation between the sample points, and for which the error decays as O (1 /n 2 ) and O (1 /n 4 ) for functions with uniformly bounded second or fourth derivatives (Cruz-Uribe and Neugebauer, 2002).”
• A Simple Solver for the Fractional Laplacian in Multiple Dimensions (2018, unknown): “This implies that the standard trapezoidal rule would exhibit second-order convergence when applied to (I); see Cruz-Uribe and Neugebauer [11].”