{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:42:56Z","timestamp":1787330576024,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>Radial basis function (RBF) interpolation is a powerful, meshfree tool for function approximation but its direct implementation might suffer from severe ill-conditioning as the shape parameter decreases. We build upon RBF-GA, a stable approach for Gaussian RBFs, and derive its representation in terms of a matrix factorization which can then be generalized to a symmetrized version. This symmetrized version requires fewer function evaluations, yields new insight into the flat limit case, and, combined with diagonal scaling, allows a further reduction of the condition number. We also propose a truncated version of the basis transformation. We conclude with numerical tests to illustrate the performance of all introduced interpolation methods.<\/jats:p>","DOI":"10.1137\/18m119207x","type":"journal-article","created":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T10:58:36Z","timestamp":1556794716000},"page":"517-541","source":"Crossref","is-referenced-by-count":5,"title":["Factorization, Symmetrization, and Truncated Transformation of Radial Basis Function-GA Stabilized Gaussian Radial Basis Functions"],"prefix":"10.1137","volume":"40","author":[{"given":"Sabine","family":"Le Borne","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,5,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2010.11.009"},{"key":"atypb2","first-page":"2214","volume":"18","author":"Chen J.","year":"2017","journal-title":"J. Mach. Learn. 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Dhillon,\n                      Memory efficient kernel approximation\n                      , in Proceedings of the 31st International Conference on Machine Learning, 2014, pp. 701-709."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.11.030"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2010.02.008"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M119207X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:13:22Z","timestamp":1787328802000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M119207X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M119207X"],"URL":"https:\/\/doi.org\/10.1137\/18m119207x","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}