{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T02:14:11Z","timestamp":1774491251418,"version":"3.50.1"},"reference-count":23,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2018,1,26]],"date-time":"2018-01-26T00:00:00Z","timestamp":1516924800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0"}],"funder":[{"DOI":"10.13039\/501100004063","name":"Knut och Alice Wallenbergs Stiftelse","doi-asserted-by":"publisher","award":["621-2014-3995"],"award-info":[{"award-number":["621-2014-3995"]}],"id":[{"id":"10.13039\/501100004063","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"publisher","award":["621-2014-3995"],"award-info":[{"award-number":["621-2014-3995"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The efficient simulation of isotropic Gaussian random fields on the unit sphere is a task encountered frequently in numerical applications. A fast algorithm based on Markov properties and fast Fourier transforms in 1d is presented that generates samples on an <jats:inline-formula id=\"j_mcma-2018-0001_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>n<\/m:mi>\n                              <m:mo>\u00d7<\/m:mo>\n                              <m:mi>n<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2018-0001_eq_0220.png\"\/>\n                        <jats:tex-math>{n\\times n}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> grid in <jats:inline-formula id=\"j_mcma-2018-0001_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi mathvariant=\"normal\">O<\/m:mi>\n                              <m:mo>\u2061<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mrow>\n                                    <m:msup>\n                                       <m:mi>n<\/m:mi>\n                                       <m:mn>2<\/m:mn>\n                                    <\/m:msup>\n                                    <m:mo>\u2062<\/m:mo>\n                                    <m:mrow>\n                                       <m:mi>log<\/m:mi>\n                                       <m:mo>\u2061<\/m:mo>\n                                       <m:mi>n<\/m:mi>\n                                    <\/m:mrow>\n                                 <\/m:mrow>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2018-0001_eq_0167.png\"\/>\n                        <jats:tex-math>{\\operatorname{O}(n^{2}\\log n)}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>. Furthermore, an efficient method to set up the necessary conditional covariance matrices is derived and simulations demonstrate the performance of the algorithm. An open source implementation of the code has been made available at <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"https:\/\/github.com\/pec27\/smerfs\">https:\/\/github.com\/pec27\/smerfs<\/jats:ext-link>.<\/jats:p>","DOI":"10.1515\/mcma-2018-0001","type":"journal-article","created":{"date-parts":[[2018,1,26]],"date-time":"2018-01-26T10:00:41Z","timestamp":1516960841000},"page":"1-11","source":"Crossref","is-referenced-by-count":16,"title":["Fast generation of isotropic Gaussian random fields on the sphere"],"prefix":"10.1515","volume":"24","author":[{"given":"Peter E.","family":"Creasey","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy , University of California , Riverside , CA 92507 , USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2661-533X","authenticated-orcid":false,"given":"Annika","family":"Lang","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences , Chalmers University of Technology & University of Gothenburg , 412 96 G\u00f6teborg , Sweden"}]}],"member":"374","published-online":{"date-parts":[[2018,1,26]]},"reference":[{"key":"2023040100385721595_j_mcma-2018-0001_ref_001","unstructured":"M.  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O\u2019Donnell,\nObservation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,\nOptics Commun. 61 (1987), no. 2, 91\u201395.","DOI":"10.1016\/0030-4018(87)90225-2"},{"key":"2023040100385721595_j_mcma-2018-0001_ref_012","doi-asserted-by":"crossref","unstructured":"G. S. P.  Miller,\nThe definition and rendering of terrain maps,\nSIGGRAPH Comput. Graph. 20 (1986), no. 4, 39\u201348.","DOI":"10.1145\/15886.15890"},{"key":"2023040100385721595_j_mcma-2018-0001_ref_013","doi-asserted-by":"crossref","unstructured":"J.  Moura and S.  Goswami,\nGauss\u2013Markov random fields (CMrf) with continuous indices,\nIEEE Trans. Inform. Theory 43 (1997), no. 5, 1560\u20131573.","DOI":"10.1109\/18.623152"},{"key":"2023040100385721595_j_mcma-2018-0001_ref_014","doi-asserted-by":"crossref","unstructured":"T.  Nousiainen and G. M.  McFarquhar,\nLight scattering by quasi-spherical ice crystals,\nJ. 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