{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T05:03:03Z","timestamp":1783400583977,"version":"3.54.6"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:p> In this paper, we present an algorithm for multivariate interpolation of scattered data sets lying in convex domains [Formula: see text], for any [Formula: see text]. To organize the points in a multidimensional space, we build a [Formula: see text]-tree space-partitioning data structure, which is used to efficiently apply a partition of unity interpolant. This global scheme is combined with local radial basis function (RBF) approximants and compactly supported weight functions. A detailed description of the algorithm for convex domains and a complexity analysis of the computational procedures are also considered. Several numerical experiments show the performances of the interpolation algorithm on various sets of Halton data points contained in [Formula: see text], where [Formula: see text] can be any convex domain, like a 2D polygon or a 3D polyhedron. Finally, an application to topographical data contained in a pentagonal domain is presented. <\/jats:p>","DOI":"10.1142\/s1793962315500348","type":"journal-article","created":{"date-parts":[[2015,7,24]],"date-time":"2015-07-24T03:08:18Z","timestamp":1437707298000},"page":"1550034","source":"Crossref","is-referenced-by-count":18,"title":["Partition of unity interpolation on multivariate convex domains"],"prefix":"10.1142","volume":"06","author":[{"given":"R.","family":"Cavoretto","sequence":"first","affiliation":[{"name":"Department of Mathematics \u201cGiuseppe Peano\u201d, University of Torino, via Carlo Alberto 10, 10123 Torino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"De Rossi","sequence":"additional","affiliation":[{"name":"Department of Mathematics \u201cGiuseppe Peano\u201d, University of Torino, via Carlo Alberto 10, 10123 Torino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"Perracchione","sequence":"additional","affiliation":[{"name":"Department of Mathematics \u201cGiuseppe Peano\u201d, University of Torino, via Carlo Alberto 10, 10123 Torino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2015,12,29]]},"reference":[{"key":"S1793962315500348BIB001","author":"Chen Y.","year":"2015","journal-title":"J. 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