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The accuracy of the constructed rules increases with increasing frequency of the integrand. For a fixed frequency, the accuracy can be improved by incorporating more derivatives of the integrand. The results are illustrated numerically for Fourier integrals on a circle and on the unit ball, and for more general oscillators on a rectangular domain.<\/p>","DOI":"10.1090\/s0025-5718-07-01937-0","type":"journal-article","created":{"date-parts":[[2007,7,26]],"date-time":"2007-07-26T07:46:03Z","timestamp":1185435963000},"page":"1955-1980","source":"Crossref","is-referenced-by-count":39,"title":["The Construction of cubature rules for multivariate highly oscillatory integrals"],"prefix":"10.1090","volume":"76","author":[{"given":"Daan","family":"Huybrechs","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Vandewalle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2007,4,27]]},"reference":[{"key":"1","unstructured":"N. Bleistein and R. Handelsman. Asymptotic Expansions of Integrals. 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