Abstract
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 significant speedups on a range of hard problems, including ones with singular integrands.
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References
J. Bernsten and T.O. Espelid, A parallel global adaptive quadrature algorithm for hypercubes, Parallel Comp. 8 (1988) 313–323.
K. Burrage, An adaptive numerical integration code for a chain of transputers, Parallel Comp. 16 (1990) 305–312.
E. de Doncker and J. Kapenga, Parallel cubature on loosely coupled systems, pp. 317–327 of [4]. —.
T.O. Espelid and A. Genz (eds.),Numerical Integration (Kluwer Academic, Dordrecht, 1992).
G. Fairweather and P.M. Keast (eds.),Numerical Integration. Recent Developments, Software and Applications, NATO ASI Series C203 (Reidel, Dordrecht, 1987).
A. Genz, The numerical evaluation of multiple integrals on parallel computers, pp. 219–229 of [5]. —.
I. Gladwell, Vectorisation of one dimensional quadrature codes, pp. 230–238 of [5] —.
M.A. Malcolm and R.B. Simpson, Local versus global strategies for adaptive quadrature, ACM Trans. Math. Software 1 (1975) 129–146.
W.M. McKeeman, Adaptive numerical integration by Simpson's rule, algorithm 145, Commun. ACM 5 (1962) 604.
N.A.G.,N.A.G. Fortran Library Manual, Mark 15 (N.A.G. Ltd., Oxford, 1991).
R. Piessens, E. de Doncker, C. Überhuber and D. Kahaner,QUADPACK, A Subroutine Package for Automatic Integration (Springer, 1983).
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Both authors acknowledge the support of the EEC Esprit Basic Research Action Programme, Project 6634 (APPARC).
The second author acknowledges the support of the NATO Collaborative Research Grant 920037.
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Bull, J.M., Freeman, T.L. Parallel globally adaptive quadrature on the KSR-1. Adv Comput Math 2, 357–373 (1994). https://doi.org/10.1007/BF02521604
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DOI: https://doi.org/10.1007/BF02521604