Parallel Algorithms and Interval Selection Strategies for Globally Adaptive Quadrature

. A globally adaptive algorithm for approximating one-dimensional definite integrals on parallel computers is described. The algorithm is implemented on a Kendall Square Research KSR-1 parallel computer and numerical results are presented. The algorithm gives significant speedups on a range of hard problems, including ones with singular integrands. A number of alternatives for the interval selection strategy that is at the core of this algorithm are evaluated. 1 Introduction In an earlier paper [2] we suggest a number of parallel algorithms for approximating the definite integral I = Z b a f(x)dx; to some given absolute accuracy ffl. Here we examine the most successful of these algorithms (the DS algorithm) in more detail, focusing on the interval selection strategy that is at the heart of the algorithm. We evaluate a number of choices for this strategy on a KSR-1 virtual shared memory parallel computer. The conventional approach to numerical integration is to use a quadrature rul..