{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:30:31Z","timestamp":1750307431141,"version":"3.41.0"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2010,9,1]],"date-time":"2010-09-01T00:00:00Z","timestamp":1283299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:p>A three-dimensional automatic cubature routine, called<jats:italic>elrint3d<\/jats:italic>, is described and numerical results are presented that demonstrate its applicability across a wide range of domains and integrand types. The underlying algorithm is based on a 2<jats:italic>s<\/jats:italic>-copy lattice augmentation sequence, the seed lattice for which has been determined by exhaustive search based on optimization of index of merit and trigonometric degree of precision.<\/jats:p>","DOI":"10.1145\/1824801.1824813","type":"journal-article","created":{"date-parts":[[2010,9,28]],"date-time":"2010-09-28T17:41:41Z","timestamp":1285695701000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Algorithm 906"],"prefix":"10.1145","volume":"37","author":[{"given":"Tiancheng","family":"Li","sequence":"first","affiliation":[{"name":"La Trobe University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ian","family":"Robinson","sequence":"additional","affiliation":[{"name":"La Trobe University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2010,9]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/838250.838253"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00767-3"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/237578.237597"},{"volume-title":"Proceedings of the 2nd Computational Particle Physics Symposium (CPP\u201901)","author":"de Doncker E.","key":"e_1_2_2_4_1","unstructured":"}} de Doncker , E. , Kaugars , K. , Cucos , L. , and Zanny , R . 2001. Current status of the ParInt package for parallel multivariate integration . In Proceedings of the 2nd Computational Particle Physics Symposium (CPP\u201901) . 110--119. }}de Doncker, E., Kaugars, K., Cucos, L., and Zanny, R. 2001. Current status of the ParInt package for parallel multivariate integration. In Proceedings of the 2nd Computational Particle Physics Symposium (CPP\u201901). 110--119."},{"volume-title":"Tools, Methods and Languages for Scientific and Engineering Computation","author":"Genz A. C.","key":"e_1_2_2_5_1","unstructured":"}} Genz , A. C. 1984. Testing multidimensional integration routines . In Tools, Methods and Languages for Scientific and Engineering Computation , B. Ford, J. C. Rault, and F. Thomasset Eds., North-Holland , Amsterdam , 81--94. }}Genz, A. C. 1984. Testing multidimensional integration routines. In Tools, Methods and Languages for Scientific and Engineering Computation, B. Ford, J. C. Rault, and F. Thomasset Eds., North-Holland, Amsterdam, 81--94."},{"volume-title":"Numerical Integration: Recent Developments, Software and Applications","author":"Genz A. C.","key":"e_1_2_2_6_1","unstructured":"}} Genz , A. C. 1987. A package for testing multiple integration subroutines . In Numerical Integration: Recent Developments, Software and Applications , P. Keast and G. Fairweather Eds., D. Reidel , 337--340. }}Genz, A. C. 1987. A package for testing multiple integration subroutines. In Numerical Integration: Recent Developments, Software and Applications, P. Keast and G. Fairweather Eds., D. Reidel, 337--340."},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/0914050"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(99)00217-4"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:NUMA.0000005348.15222.6a"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.09.057"},{"key":"e_1_2_2_11_1","first-page":"689","article-title":"Numerical quadrature by the \u03b5-algorithm","volume":"26","author":"Kahaner D.","year":"1972","unstructured":"}} Kahaner , D. 1972 . Numerical quadrature by the \u03b5-algorithm . Math. Comput. 26 , 689 -- 693 . }}Kahaner, D. 1972. Numerical quadrature by the \u03b5-algorithm. Math. Comput. 26, 689--693.","journal-title":"Math. Comput."},{"key":"e_1_2_2_13_1","doi-asserted-by":"crossref","unstructured":"}} Li T. and Robinson I . 2007 . The search for a good lattice augmentation sequence in three dimensions. In Proceedings of the International Conference on Computational Science and Its Application (ICCSA3) O. Gervasi and M. L. Gavrilova Eds. Lecture Notes in Computer Science vol. 4707 . Springer 1037--1045. }} Li T. and Robinson I. 2007. The search for a good lattice augmentation sequence in three dimensions. In Proceedings of the International Conference on Computational Science and Its Application (ICCSA3) O. Gervasi and M. L. Gavrilova Eds. Lecture Notes in Computer Science vol. 4707. Springer 1037--1045.","DOI":"10.1007\/978-3-540-74484-9_90"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.05.010"},{"volume-title":"Numerical Integration: Recent Developments, Software and Applications","author":"Patterson T. N. L.","key":"e_1_2_2_15_1","unstructured":"}} Patterson , T. N. L. 1987. Testing multiple integrators . In Numerical Integration: Recent Developments, Software and Applications , P. Keast and G. Fairweather Eds., Reidel Publishing Company , 331--335. }}Patterson, T. N. L. 1987. Testing multiple integrators. In Numerical Integration: Recent Developments, Software and Applications, P. Keast and G. Fairweather Eds., Reidel Publishing Company, 331--335."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/513001.513006"},{"key":"e_1_2_2_17_1","first-page":"359","article-title":"A new variable transformation for numerical integration","volume":"112","author":"Sidi A.","year":"1993","unstructured":"}} Sidi , A. 1993 . A new variable transformation for numerical integration . Int. Series Numer. Math. 112 , 359 -- 373 . }}Sidi, A. 1993. A new variable transformation for numerical integration. Int. Series Numer. Math. 112, 359--373.","journal-title":"Int. Series Numer. Math."},{"volume-title":"Practical Extrapolation Methods: Theory and Applications","author":"Sidi A.","key":"e_1_2_2_18_1","unstructured":"}} Sidi , A. 2002. Practical Extrapolation Methods: Theory and Applications . Cambridge University Press , Cambridge, UK . }}Sidi, A. 2002. Practical Extrapolation Methods: Theory and Applications. Cambridge University Press, Cambridge, UK."},{"key":"e_1_2_2_19_1","doi-asserted-by":"crossref","unstructured":"}}Sloan I. H. and Joe S. 1994. Lattice Methods for Multiple Integration. Oxford University Press Oxford UK. }} Sloan I. H. and Joe S. 1994. Lattice Methods for Multiple Integration . Oxford University Press Oxford UK.","DOI":"10.1093\/oso\/9780198534723.001.0001"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/0724010"},{"key":"e_1_2_2_21_1","volume-title":"The Mathematica Book","author":"Wolfram S.","unstructured":"}} Wolfram , S. 1999. The Mathematica Book , 4 th Ed. Cambridge University Press , UK. }}Wolfram, S. 1999. The Mathematica Book, 4th Ed. Cambridge University Press, UK.","edition":"4"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1137\/0703007"},{"key":"e_1_2_2_23_1","doi-asserted-by":"crossref","unstructured":"}}Zaremba S. K. 1966. Good lattice points discrepancy and numerical integration. Annali di Matematica Pura ed Applicata 73 293--317. (In Italian.) }} Zaremba S. K. 1966. Good lattice points discrepancy and numerical integration. Annali di Matematica Pura ed Applicata 73 293--317. (In Italian.)","DOI":"10.1007\/BF02415091"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1824801.1824813","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1824801.1824813","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T11:39:54Z","timestamp":1750246794000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1824801.1824813"}},"subtitle":["elrint3d\u2014A Three-Dimensional Nonadaptive Automatic Cubature Routine Using a Sequence of Embedded Lattice Rules"],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["10.1145\/1824801.1824813"],"URL":"https:\/\/doi.org\/10.1145\/1824801.1824813","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"type":"print","value":"0098-3500"},{"type":"electronic","value":"1557-7295"}],"subject":[],"published":{"date-parts":[[2010,9]]},"assertion":[{"value":"2008-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-01-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-09-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}