{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:34:12Z","timestamp":1787330052703,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"name":"Spanish Research Agency (AEI) and European Union FEDER","award":["RTI2018-093521-B-C31"],"award-info":[{"award-number":["RTI2018-093521-B-C31"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this paper, we focus on the convergence analysis of the approximation of the Proper Generalized Decomposition (PGD) modes for the parameterized solution of elliptic equations. We prove that the PGD modes of the discretized problem converge to the PGD modes of the continuous problem with respect to the discretization of both the parameter set and the elliptic problem afforded. The proof is performed for composed integration quadrature formulae with respect to the parameters. We present some numerical experiments to assess this convergence and to give some indications on the rate of convergence.<\/jats:p>","DOI":"10.1137\/22m1505037","type":"journal-article","created":{"date-parts":[[2023,9,19]],"date-time":"2023-09-19T11:56:55Z","timestamp":1695124615000},"page":"A2207-A2225","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Approximation of PGD Modes to Parameterized Elliptic Problems"],"prefix":"10.1137","volume":"45","author":[{"given":"Mejdi","family":"Aza\u00efez","sequence":"first","affiliation":[{"name":"Bordeaux University, Bordeaux INP and I2M (UMR CNRS 5295), 33400 Talence, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tom\u00e1s Chac\u00f3n","family":"Rebollo","sequence":"additional","affiliation":[{"name":"Departamento EDAN & IMUS, Universidad de Sevilla, Seville, Spain."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2489-6126","authenticated-orcid":true,"given":"Isabel S\u00e1nchez","family":"Mu\u00f1oz","sequence":"additional","affiliation":[{"name":"Departamento Matem\u00e1tica Aplicada I, Universidad de Sevilla, Seville, Spain."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,9,19]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnnfm.2006.07.007"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2015.02.019"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/17M1137164"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s40324-019-00198-7"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(90)90011-A"},{"key":"ref6","first-page":"209","volume":"5","author":"Bernardi C.","year":"1997","journal-title":"Handbook Numer. 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Khachatryan , On the Convergence of Alternating Least Squares Optimisation in Tensor Format Representations, preprint, arXiv:1506.00062v1, 2015."},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-011-0437-5"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1432-8"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2011.04.019"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/110843587"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/130938207"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1505037","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:45:53Z","timestamp":1787327153000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1505037"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,19]]},"references-count":20,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10,31]]}},"alternative-id":["10.1137\/22M1505037"],"URL":"https:\/\/doi.org\/10.1137\/22m1505037","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,19]]}}}