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SINGINT: automatic numerical integration of singular integrands. (English) Zbl 1196.65214
Summary: We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion and are runtime and memory optimized, respectively. SINGINT, a C implementation of the algorithms, is introduced and its utilization in the calculation of particle scattering amplitudes is exemplified.
65Y99 Computer aspects of numerical algorithms
Full Text: DOI
[1] Piessens, R., Quadpack, (1983), Springer-Verlag
[2] Press, W.H., Numerical recipes, (1992), Cambridge University Press · Zbl 0778.65003
[3] Espelid, T.O.; Genz, A.; Singstad, K.; Espelid, T.O.; Lyness, J.N., Numerical algorithms, J. comp. appl. math., Math. comp., 30, 1, (1976), and references therein
[4] James, F.; Hoogland, J.; Kleiss, R., Comp. phys. comm., 99, 180, (1997)
[5] Bratley, P.; Fox, B.L.; Niederreiter, H., ACM trans. model. comp. sim., 2, 195, (1992)
[6] Berntsen, J.; Espelid, T.O.; Genz, A., ACM trans. math. software, ACM trans. math. software, 17, 452, (1991)
[7] T. Binoth, G. Heinrich, N. Kauer, Preprint Edinburgh 2002/16 (2002), arXiv:hep-ph/0210023
[8] Lepage, G.P., J. comput. phys., 27, 192, (1978), Preprint CLNS-80/447 (1980)
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