{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T19:05:00Z","timestamp":1788462300618,"version":"build-2803163510"},"reference-count":19,"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":[[2010,1]]},"abstract":"<jats:p>We present a new nonlinear optimization procedure for the computation of generalized Gaussian quadratures for a broad class of square integrable functions on intervals. While some of the components of this algorithm have been previously published, we present a simple and robust scheme for the determination of a sparse solution to an underdetermined nonlinear optimization problem which replaces the continuation scheme of the previously published works. The new algorithm successfully computes generalized Gaussian quadratures in a number of instances in which the previous algorithms fail. Four applications of our scheme to computational physics are presented: the construction of discrete plane wave expansions for the Helmholtz Green's function, the design of linear array antennae, the computation of a quadrature for the discretization of Laplace boundary integral equations on certain domains with corners, and the construction of quadratures for the discretization of Laplace and Helmholtz boundary integral equations on smooth surfaces.<\/jats:p>","DOI":"10.1137\/080737046","type":"journal-article","created":{"date-parts":[[2010,6,20]],"date-time":"2010-06-20T21:18:25Z","timestamp":1277068705000},"page":"1761-1788","source":"Crossref","is-referenced-by-count":107,"title":["A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures"],"prefix":"10.1137","volume":"32","author":[{"given":"James","family":"Bremer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zydrunas","family":"Gimbutas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vladimir","family":"Rokhlin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,6,18]]},"reference":[{"key":"R1","unstructured":"M. Abramowitz and I. Stegun, eds.\n                      Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables\n                      , National Bureau of Standards, U.S. Government Printing Office, Washington, DC, 1964."},{"key":"R2","doi-asserted-by":"crossref","unstructured":"K. Atkinson,\n                      The Numerical Solution of Integral Equations of the Second Kind\n                      , Cambridge University Press, Cambridge, 1997.","DOI":"10.1017\/CBO9780511626340"},{"key":"R3","unstructured":"C. A. Balanis,\n                      Antenna Theory,\n                      3rd ed., John Wiley and Sons, Hoboken, NJ, 2005."},{"key":"R4","doi-asserted-by":"crossref","unstructured":"A. Bj\u00f6rck,\n                      Numerical Methods for Least Squares Problems\n                      , SIAM, Philadephia, 1996.","DOI":"10.1137\/1.9781611971484"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623498349796"},{"key":"R6","unstructured":"J. Dennis and R. Schnabel,\n                      Numerical Methods for Unconstrained Optimization and Nonlinear Equations\n                      , Prentice-Hall, Englewood Cliffs, NJ, 1983."},{"key":"R7","unstructured":"G. Golub and C. V. Loan,\n                      Matrix Computations\n                      , Johns Hopkins University Press, Baltimore, 1983."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1109\/99.714591"},{"key":"R9","unstructured":"P. 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Feshbach,\n                      Methods of Mathematical Physics\n                      , Feshbach Publishing,Minneapolis, MN, 1981."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596310779"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080737046","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:46:38Z","timestamp":1787330798000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080737046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080737046"],"URL":"https:\/\/doi.org\/10.1137\/080737046","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}