{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:47Z","timestamp":1787337287418,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>Slater integrals are two\u2010dimensional radial integrals whose integrand is constructed from normalized eigenfunctions of the Schr\u00f6dinger equation. These integrals occur in many atomic structure and scattering computations. However, in two\u2010dimensional R\u2010matrix propagation they represent a significant computational bottleneck. The problem involves two steps, that is, the numerical solution of the Schr\u00f6dinger equation and the computation of the integrals, respectively. By exploiting the characteristic features of the problem we seek to devise a two\u2010stage computational strategy, where the second stage is influenced and informed by the first. In particular, we focus on the development of extended frequency\u2010dependent quadrature rules (EFDQRs) that improve the accuracy and significantly reduce the computation time of the integrals. The performance of these ad hoc rules is examined and compared to the currently used Newton\u2013Cotes method in the construction of Hamiltonian matrices involving up to $300\\times10^6$ integrals. A gain of two orders of magnitude in the CPU time is obtained.<\/jats:p>","DOI":"10.1137\/050641004","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:30:58Z","timestamp":1156433458000},"page":"1252-1274","source":"Crossref","is-referenced-by-count":6,"title":["Fast Computation of the Slater Integrals"],"prefix":"10.1137","volume":"28","author":[{"given":"L. Gr.","family":"Ixaru","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"N.\u2010S.","family":"Scott","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. P.","family":"Scott","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"M. Abramowitz and I. A. Stegun,\n                      Handbook of Mathematical Functions\n                      , 8th ed., Dover, New York, 1972."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.63.050701"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1145\/355791.355792"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1088\/0953-4075\/29\/1\/015"},{"key":"R5","unstructured":"K. H. Becker, C. W. McCurdy, T. M. Orlando, and T. N. 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Burke,\n                      2DRMP\u2010G: Migrating a large\u2010scale numerical mathematical application to a grid environment\n                      , in High Performance Computing in Computational Science (VECPAR 2004), Lecture Notes in Comput. Sci. 3402, M. Dayd\u00e9 et al., eds., Springer, Berlin, 2005, pp. 233\u2013246."},{"key":"R11","unstructured":"CSAR (Computer Services for Academic Research), UK National Supercomputing Service, University of Manchester, Manchester, UK, http:\/\/www.cfs.ac.uk\/."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.54.561"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4655(98)00137-4"},{"key":"R14","unstructured":"HPCx, UK National Supercomputing Service, Edinburgh, UK, http:\/\/www.hpcx.ac.uk\/."},{"key":"R15","unstructured":"Harvey Itanium 2 cluster, Queen\u2019s University Belfast, Belfast, UK, http:\/\/harvey.am.qub.ac.uk\/."},{"key":"R16","unstructured":"L. Gr. 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