{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T14:27:50Z","timestamp":1791901670964,"version":"4.3.4"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2002,5,1]],"date-time":"2002-05-01T00:00:00Z","timestamp":1020211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Science and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["OGP 105367"],"award-info":[{"award-number":["OGP 105367"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Science and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["OGP 0002151"],"award-info":[{"award-number":["OGP 0002151"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2002,5,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>It is occasionally necessary to smooth data over domains in \u211d2 with complex irregular boundaries or interior holes. Traditional methods of smoothing which rely on the Euclidean metric or which measure smoothness over the entire real plane may then be inappropriate. This paper introduces a bivariate spline smoothing function defined as the minimizer of a penalized sum-of-squares functional. The roughness penalty is based on a partial differential operator and is integrated only over the problem domain by using finite element analysis. The method is motivated by and applied to two sample smoothing problems and is compared with the thin plate spline.<\/jats:p>","DOI":"10.1111\/1467-9868.00339","type":"journal-article","created":{"date-parts":[[2003,5,6]],"date-time":"2003-05-06T11:13:15Z","timestamp":1052219595000},"page":"307-319","source":"Crossref","is-referenced-by-count":114,"title":["Spline Smoothing over Difficult Regions"],"prefix":"10.1093","volume":"64","author":[{"given":"Tim","family":"Ramsay","sequence":"first","affiliation":[{"name":"McLaughlin Centre for Population Health Risk Assessment , Ottawa , Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2002,6,20]]},"reference":[{"key":"2023040108505028600_","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-07233-2","volume-title":"Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics","author":"Braess","year":"1997"},{"key":"2023040108505028600_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4338-8","volume-title":"The Mathematical Theory of Finite Elements","author":"Brenner","year":"1994"},{"key":"2023040108505028600_","volume-title":"Finite Elements: a Second Course","author":"Carey","year":"1983"},{"key":"2023040108505028600_","first-page":"175","article-title":"Applications of spatial smoothing to survey data","volume":"22","author":"Cowling","year":"1996","journal-title":"Surv. 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