Adaptive quadrature: Convergence of parallel and sequential algorithms

Adaptive Quadrature: Convergence of Parallel and Sequential Algorithms

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 represen...

Parallel Algorithms for Adaptive Quadrature - Convergence

Parallel Quadrature Algorithms for Singularintegralsj

Reducing Ranking Effects in Parallel Adaptive Quadrature

We develop parallel one-dimensional globally adaptive quadrature algorithms, building on NAG code D01AKF. Our most eeective strategy replaces D01AKF's error estimate ranking strategy by a tabulation approach. D01AKF uses 61-point Gauss-Kronrod (GK) quadrature. We also use the 21-point GK rule. A fuller discussion, with expanded results, is given in 7].

Parallel Globally Adaptive Quadrature on the KSR

New algorithms for parallel one-dimensional globally adaptive quadrature are developed. The algorithms are implemented on a Kendall Square Research KSR-1 parallel computer and numerical results are presented. The most successful algorithm gives signiicant speedups on a range of hard problems, including ones with singular integrands.