Adaptive Quadrature: Convergence of Parallel and Sequential Algorithms
نویسنده
چکیده
to adapt their estimates to the particular nature of the integrand f(x). Within the past five years experimental evidence has appeared to suggest that adaptive quadrature algorithms are significantly superior to traditional quadrature formulas because they have a much wider domain of efficient applicability with little sacrifice in computational effort. A metalgorithm is an abstraction representing a large class of algorithms and is used to discuss and analyze the properties of adaptive quadrature algorithms. A novel feature of these algorithms is the important role that data structures (for the interval collection) play in their behavior. A study of reasonable selections of components for the metalgorithm shows that there are from 1 to 10 million potentially interesting, significantly distinct adaptive quadrature algorithms. This situation illustrates the extreme difficulty of the common problem of selecting the "best" algorithm for a particular computation. Our purpose is to announce convergence results for a variety of adaptive quadrature algorithms (including all 10 million mentioned above). Roughly
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