{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T07:16:12Z","timestamp":1771485372659,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s10915-020-01159-3","type":"journal-article","created":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T14:07:40Z","timestamp":1581948460000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["An Efficient Trivariate Algorithm for Tetrahedral Shepard Interpolation"],"prefix":"10.1007","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6076-4115","authenticated-orcid":false,"given":"R.","family":"Cavoretto","sequence":"first","affiliation":[]},{"given":"A.","family":"De Rossi","sequence":"additional","affiliation":[]},{"given":"F.","family":"Dell\u2019Accio","sequence":"additional","affiliation":[]},{"given":"F.","family":"Di Tommaso","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,17]]},"reference":[{"key":"1159_CR1","first-page":"35","volume":"318","author":"G Allasia","year":"2018","unstructured":"Allasia, G., Cavoretto, R., De Rossi, A.: Hermite-Birkhoff interpolation on scattered data on the sphere and other manifolds. Appl. Math. Comput. 318, 35\u201350 (2018)","journal-title":"Appl. Math. Comput."},{"key":"1159_CR2","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1145\/293347.293348","volume":"45","author":"S Arya","year":"1998","unstructured":"Arya, S., Mount, D.M., Netanyahu, N.S., Silverman, R., Wu, A.Y.: An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J. ACM 45, 891\u2013923 (1998)","journal-title":"J. ACM"},{"key":"1159_CR3","first-page":"111","volume":"20","author":"M Bozzini","year":"2002","unstructured":"Bozzini, M., Rossini, M.: Testing methods for 3D scattered data interpolation. Monogr. Real Acad. Ci. Exact. Fis.-Quim. Nat. Zaragoza 20, 111\u2013135 (2002)","journal-title":"Monogr. Real Acad. Ci. Exact. Fis.-Quim. Nat. Zaragoza"},{"key":"1159_CR4","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.aml.2018.10.026","volume":"90","author":"R Cavoretto","year":"2019","unstructured":"Cavoretto, R., De Rossi, A.: Adaptive meshless refinement schemes for RBF-PUM collocation. Appl. Math. Lett. 90, 131\u2013138 (2019)","journal-title":"Appl. Math. Lett."},{"key":"1159_CR5","first-page":"124824","volume":"369","author":"R Cavoretto","year":"2020","unstructured":"Cavoretto, R., De Rossi, A.: Error indicators and refinement strategies for solving Poisson problems through a RBF partition of unity collocation scheme. Appl. Math. Comput. 369, 124824 (2020)","journal-title":"Appl. Math. Comput."},{"key":"1159_CR6","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/j.cam.2018.03.012","volume":"354","author":"R Cavoretto","year":"2019","unstructured":"Cavoretto, R., De Rossi, A., Dell\u2019Accio, F., Di Tommaso, F.: Fast computation of triangular Shepard interpolants. J. Comput. Appl. Math. 354, 457\u2013470 (2019)","journal-title":"J. Comput. Appl. Math."},{"key":"1159_CR7","doi-asserted-by":"publisher","first-page":"2568","DOI":"10.1016\/j.camwa.2016.04.021","volume":"71","author":"R Cavoretto","year":"2016","unstructured":"Cavoretto, R., De Rossi, A., Perracchione, E.: Efficient computation of partition of unity interpolants through a block-based searching technique. Comput. Math. Appl. 71, 2568\u20132584 (2016)","journal-title":"Comput. Math. Appl."},{"key":"1159_CR8","first-page":"32","volume":"9","author":"F Dell\u2019Accio","year":"2016","unstructured":"Dell\u2019Accio, F., Di Tommaso, F.: Scattered data interpolation by Shepard\u2019s like methods: Classical results and recent advances. Dolomites Res. Notes Approx. 9, 32\u201344 (2016)","journal-title":"Dolomites Res. Notes Approx."},{"key":"1159_CR9","first-page":"1","volume":"12","author":"F Dell\u2019Accio","year":"2019","unstructured":"Dell\u2019Accio, F., Di Tommaso, F.: Rate of convergence of multinode Shepard operators. Dolomites Res. Notes Approx. 12, 1\u20136 (2019)","journal-title":"Dolomites Res. Notes Approx."},{"key":"1159_CR10","first-page":"359","volume":"36","author":"F Dell\u2019Accio","year":"2016","unstructured":"Dell\u2019Accio, F., Di Tommaso, F., Hormann, K.: On the approximation order of triangular Shepard interpolation. IMA J. Numer. Anal. 36, 359\u2013379 (2016)","journal-title":"IMA J. Numer. Anal."},{"key":"1159_CR11","doi-asserted-by":"publisher","DOI":"10.1142\/6437","volume-title":"Meshfree Approximation Methods with Matlab","author":"GE Fasshauer","year":"2007","unstructured":"Fasshauer, G.E.: Meshfree Approximation Methods with Matlab. World Scientific, Singapore (2007)"},{"issue":"3","key":"1159_CR12","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/S0925-7721(02)00123-2","volume":"25","author":"MJ Golin","year":"2003","unstructured":"Golin, M.J., Na, H.S.: On the average complexity of 3d-voronoi diagrams of random points on convex polytopes. Comput. Geom. 25(3), 197\u2013231 (2003). https:\/\/doi.org\/10.1016\/S0925-7721(02)00123-2","journal-title":"Comput. Geom."},{"key":"1159_CR13","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1016\/S0377-0427(01)00485-X","volume":"140","author":"D Lazzaro","year":"2002","unstructured":"Lazzaro, D., Montefusco, L.B.: Radial basis functions for the multivariate interpolation of large scattered data sets. J. Comput. Appl. Math. 140, 521\u2013536 (2002)","journal-title":"J. Comput. Appl. Math."},{"key":"1159_CR14","first-page":"99","volume-title":"Surfaces in Computer Aided Geometric Design","author":"FF Little","year":"1983","unstructured":"Little, F.F.: Convex combination surfaces. In: Barnhill, R.E., Boehm, W. (eds.) Surfaces in Computer Aided Geometric Design, vol. 1479, pp. 99\u2013108. North-Holland, Amsterdam (1983)"},{"key":"1159_CR15","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1145\/45054.45055","volume":"14","author":"RJ Renka","year":"1988","unstructured":"Renka, R.J.: Multivariate interpolation of large sets of scattered data. ACM Trans. Math. Softw. 14, 139\u2013148 (1988)","journal-title":"ACM Trans. Math. Softw."},{"key":"1159_CR16","doi-asserted-by":"crossref","unstructured":"Shepard, D.: A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings of the 1968 23rd ACM National Conference, ACM\u201968, pp. 517\u2013524. ACM, New York, NY, USA (1968)","DOI":"10.1145\/800186.810616"},{"key":"1159_CR17","volume-title":"Theory of Equations","author":"JV Uspensky","year":"1948","unstructured":"Uspensky, J.V.: Theory of Equations. McGraw-Hill, New York (1948)"},{"key":"1159_CR18","volume-title":"Scattered Data Approximation. Cambridge Monographs on Applied and Computational Mathematics","author":"H Wendland","year":"2005","unstructured":"Wendland, H.: Scattered Data Approximation. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge (2005)"},{"key":"1159_CR19","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1016\/j.apnum.2010.12.011","volume":"61","author":"M Zhang","year":"2011","unstructured":"Zhang, M., Liang, X.Z.: On a Hermite interpolation on the sphere. Appl. Numer. Math. 61, 666\u2013674 (2011)","journal-title":"Appl. Numer. Math."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01159-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-020-01159-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-020-01159-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,18]],"date-time":"2021-02-18T23:54:17Z","timestamp":1613692457000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-020-01159-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,17]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["1159"],"URL":"https:\/\/doi.org\/10.1007\/s10915-020-01159-3","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,17]]},"assertion":[{"value":"24 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 February 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"57"}}