Probabilistic analysis of numerical integration algorithms
The author studies the expected error of approximation for a class of adaptive numerical integration methods. He analyzes a heuristic error criterion that can be used to choose the initial approximation and serve as the termination and adaptation criterion with a rigorous mathematical (probabilistic) basis. The probabilistic model assumes that the functions are distributed according to a k-fold Wiener measure on an appropriate space of k-times continuously differentiable functions.
scientific article; zbMATH DE number 4195025
scientific article