{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:57:50Z","timestamp":1776841070011,"version":"3.51.2"},"reference-count":53,"publisher":"American Mathematical Society (AMS)","issue":"358","license":[{"start":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T00:00:00Z","timestamp":1773187200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>For radial basis function (RBF) kernel interpolation of scattered data, Schaback [Adv. Comput. Math. 3 (1995), pp.\u00a0251\u2013264] proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He referred to this finding as an \u201cuncertainty relation,\u201d an undesirable consequence of which is that RBF kernel interpolation is susceptible to noisy data. In this paper, we propose and study a distributed interpolation method to manage and quantify the uncertainty brought on by interpolating noisy spherical data of non-negligible magnitude. We also present numerical simulation results showing that our method is practical and robust in handling noisy data from challenging computing environments.<\/p>","DOI":"10.1090\/mcom\/4076","type":"journal-article","created":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T09:11:47Z","timestamp":1741684307000},"page":"969-998","source":"Crossref","is-referenced-by-count":1,"title":["Distributed uncertainty quantification of kernel interpolation on spheres"],"prefix":"10.1090","volume":"95","author":[{"given":"Shao-Bo","family":"Lin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingping","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Di","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2025,3,11]]},"reference":[{"key":"1","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0653-8","volume-title":"Matrix analysis","volume":"169","author":"Bhatia, Rajendra","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/0387948465"},{"issue":"1","key":"2","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s00365-006-0629-4","article-title":"Numerical integration over spheres of arbitrary dimension","volume":"25","author":"Brauchart, Johann S.","year":"2007","journal-title":"Constr. 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